A ball is hit at 64 ft/s at 60° from 2 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth.

x = 32t,; y = -16t^2 + 32sqrt(3) t + 2;; about 112.0 ft

An arrow is shot at 70 ft/s at 60° from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth.

x = 35t,; y = -16t^2 + 35sqrt(3) t;; about 132.6 ft

A ball is thrown at 114 ft/s at 45° from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth.

x = 57sqrt(2) t,; y = -16t^2 + 57sqrt(2) t + 5;; about 411.1 ft

A ball is thrown at 48 ft/s at 30° from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth.

x = 24sqrt(3) t,; y = -16t^2 + 24t;; about 62.4 ft

A soccer ball is kicked at 90 ft/s at 30° from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth.

x = 45sqrt(3) t,; y = -16t^2 + 45t + 5;; about 227.6 ft

A ball is hit at 84 ft/s at 45° from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth.

x = 42sqrt(2) t,; y = -16t^2 + 42sqrt(2) t;; about 220.5 ft

A ball is kicked at 12~m/s at 40° from 1 m above the ground. Write parametric equations (g = 9.8 m/s^2) and find how far it travels, to the nearest tenth of a meter.

x = 12cos 40° t,; y = -4.9t^2 + 12sin 40° t + 1;; about 15.6 m

A ball is hit at 88~ft/s at 45° from 6 ft above the ground (g = 32 ft/s^2). To the nearest tenth, find the time in the air, the horizontal distance, the time of the greatest height, and the greatest height.

4.0 s, 247.9 ft, 1.9 s, 66.5 ft

A ball is launched from the ground at 64~ft/s at 45° (g = 32 ft/s^2). Sketch its path and give the horizontal distance and the greatest height, to the nearest tenth.

Distance 128.0 ft; greatest height 32.0 ft

Worksheets · Algebra 2

Projectile motion worksheet for Algebra 2

In Algebra 2 projectile problems use h(t) = -16t² + v₀t + h₀ and test several quadratic skills at once: the vertex for the top, the quadratic formula for landing, and solving h(t) equal to a given height, which often has two answers. Some go further with launch angles and parametric equations.

Also taught in Precalculus and Algebra 1, each at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Projectile Motion Date Period Answer each question. Round to the nearest tenth. Find the greatest height A rocket is fired straight up, and $h (t) = - 16 t^{2} + 120 t + 20$ gives the height in feet $t$ seconds after launch. How high does it go? When a ball is thrown straight up, $h (t) = - 16 t^{2} + 96 t + 35$ gives the height in feet $t$ seconds after launch. What is its maximum height? A water balloon is launched upward at 104 ft/s from a balcony 35 ft high. $h (t) = - 16 t^{2} + 104 t + 35$ gives the height in feet $t$ seconds after launch. Find the greatest height. A stone is tossed up at 88 ft/s from a bridge 15 ft above the water. $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. Find the greatest height. A water balloon is launched upward at 128 ft/s from a balcony 45 ft high. $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. How high does it go? Find when it lands A baseball is hit straight up at 80 ft/s from 25 ft above the field. $h (t) = - 16 t^{2} + 80 t + 25$ gives the height in feet $t$ seconds after launch. When does it hit the field? In a physics lab, an arrow is shot straight up; $h (t) = - 16 t^{2} + 96 t + 55$ gives the height in feet $t$ seconds after launch. How many seconds after launch does it land? For a ball thrown straight up, $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land? In a physics lab, a rocket is fired straight up; $h (t) = - 16 t^{2} + 96 t + 60$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land? For an arrow shot straight up, $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. When does it land? Write parametric equations for a launch A ball is hit at 64 ft/s at $60^{\circ}$ from 2 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. An arrow is shot at 70 ft/s at $60^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth. A ball is thrown at 114 ft/s at $45^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. A ball is thrown at 48 ft/s at $30^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth. A soccer ball is kicked at 90 ft/s at $30^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. Find when it reaches a given height $h (t) = - 16 t^{2} + 112 t + 25$ . When is the object 217 ft high? $h (t) = - 16 t^{2} + 96 t$ . When is the object 80 ft high? $h (t) = - 16 t^{2} + 96 t + 24$ . When is the object 152 ft high? $h (t) = - 16 t^{2} + 112 t$ . When is the object 160 ft high? $h (t) = - 16 t^{2} + 80 t + 17$ . When is the object 113 ft high? Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Projectile Motion

Date Period

Answer each question. Round to the nearest tenth.

Find the greatest height
A rocket is fired straight up, and $h (t) = - 16 t^{2} + 120 t + 20$ gives the height in feet $t$ seconds after launch. How high does it go?
When a ball is thrown straight up, $h (t) = - 16 t^{2} + 96 t + 35$ gives the height in feet $t$ seconds after launch. What is its maximum height?
A water balloon is launched upward at 104 ft/s from a balcony 35 ft high. $h (t) = - 16 t^{2} + 104 t + 35$ gives the height in feet $t$ seconds after launch. Find the greatest height.
A stone is tossed up at 88 ft/s from a bridge 15 ft above the water. $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. Find the greatest height.
A water balloon is launched upward at 128 ft/s from a balcony 45 ft high. $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. How high does it go?

Find when it lands
A baseball is hit straight up at 80 ft/s from 25 ft above the field. $h (t) = - 16 t^{2} + 80 t + 25$ gives the height in feet $t$ seconds after launch. When does it hit the field?
In a physics lab, an arrow is shot straight up; $h (t) = - 16 t^{2} + 96 t + 55$ gives the height in feet $t$ seconds after launch. How many seconds after launch does it land?
For a ball thrown straight up, $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land?
In a physics lab, a rocket is fired straight up; $h (t) = - 16 t^{2} + 96 t + 60$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land?
For an arrow shot straight up, $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. When does it land?

Write parametric equations for a launch
A ball is hit at 64 ft/s at $60^{\circ}$ from 2 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth.
An arrow is shot at 70 ft/s at $60^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth.
A ball is thrown at 114 ft/s at $45^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth.
A ball is thrown at 48 ft/s at $30^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth.
A soccer ball is kicked at 90 ft/s at $30^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth.

Find when it reaches a given height
$h (t) = - 16 t^{2} + 112 t + 25$ . When is the object 217 ft high?
$h (t) = - 16 t^{2} + 96 t$ . When is the object 80 ft high?
$h (t) = - 16 t^{2} + 96 t + 24$ . When is the object 152 ft high?
$h (t) = - 16 t^{2} + 112 t$ . When is the object 160 ft high?
$h (t) = - 16 t^{2} + 80 t + 17$ . When is the object 113 ft high?



Sigma Prep · sigmaprep.io/worksheets Name Projectile MotionAnswer keyVersion 2 Date Period Answer each question. Round to the nearest tenth. Find the greatest height A rocket is fired straight up, and $h (t) = - 16 t^{2} + 120 t + 20$ gives the height in feet $t$ seconds after launch. How high does it go? $245.0$ ft When a ball is thrown straight up, $h (t) = - 16 t^{2} + 96 t + 35$ gives the height in feet $t$ seconds after launch. What is its maximum height? $179.0$ ft A water balloon is launched upward at 104 ft/s from a balcony 35 ft high. $h (t) = - 16 t^{2} + 104 t + 35$ gives the height in feet $t$ seconds after launch. Find the greatest height. $204.0$ ft A stone is tossed up at 88 ft/s from a bridge 15 ft above the water. $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. Find the greatest height. $136.0$ ft A water balloon is launched upward at 128 ft/s from a balcony 45 ft high. $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. How high does it go? $301.0$ ft Find when it lands A baseball is hit straight up at 80 ft/s from 25 ft above the field. $h (t) = - 16 t^{2} + 80 t + 25$ gives the height in feet $t$ seconds after launch. When does it hit the field? $5.3$ s In a physics lab, an arrow is shot straight up; $h (t) = - 16 t^{2} + 96 t + 55$ gives the height in feet $t$ seconds after launch. How many seconds after launch does it land? $6.5$ s For a ball thrown straight up, $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land? $8.3$ s In a physics lab, a rocket is fired straight up; $h (t) = - 16 t^{2} + 96 t + 60$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land? $6.6$ s For an arrow shot straight up, $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. When does it land? $5.7$ s Write parametric equations for a launch A ball is hit at 64 ft/s at $60^{\circ}$ from 2 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 32 t$ , $y = - 16 t^{2} + 32 \sqrt{3} t + 2$ ; about 112.0 ft An arrow is shot at 70 ft/s at $60^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 35 t$ , $y = - 16 t^{2} + 35 \sqrt{3} t$ ; about 132.6 ft A ball is thrown at 114 ft/s at $45^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 57 \sqrt{2} t$ , $y = - 16 t^{2} + 57 \sqrt{2} t + 5$ ; about 411.1 ft A ball is thrown at 48 ft/s at $30^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 24 \sqrt{3} t$ , $y = - 16 t^{2} + 24 t$ ; about 62.4 ft A soccer ball is kicked at 90 ft/s at $30^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 45 \sqrt{3} t$ , $y = - 16 t^{2} + 45 t + 5$ ; about 227.6 ft Find when it reaches a given height $h (t) = - 16 t^{2} + 112 t + 25$ . When is the object 217 ft high? $t = 3$ s and $t = 4$ s $h (t) = - 16 t^{2} + 96 t$ . When is the object 80 ft high? $t = 1$ s and $t = 5$ s $h (t) = - 16 t^{2} + 96 t + 24$ . When is the object 152 ft high? $t = 2$ s and $t = 4$ s $h (t) = - 16 t^{2} + 112 t$ . When is the object 160 ft high? $t = 2$ s and $t = 5$ s $h (t) = - 16 t^{2} + 80 t + 17$ . When is the object 113 ft high? $t = 2$ s and $t = 3$ s Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Projectile MotionAnswer keyVersion 2

Date Period

Answer each question. Round to the nearest tenth.

Find the greatest height
A rocket is fired straight up, and $h (t) = - 16 t^{2} + 120 t + 20$ gives the height in feet $t$ seconds after launch. How high does it go? $245.0$ ft
When a ball is thrown straight up, $h (t) = - 16 t^{2} + 96 t + 35$ gives the height in feet $t$ seconds after launch. What is its maximum height? $179.0$ ft
A water balloon is launched upward at 104 ft/s from a balcony 35 ft high. $h (t) = - 16 t^{2} + 104 t + 35$ gives the height in feet $t$ seconds after launch. Find the greatest height. $204.0$ ft
A stone is tossed up at 88 ft/s from a bridge 15 ft above the water. $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. Find the greatest height. $136.0$ ft
A water balloon is launched upward at 128 ft/s from a balcony 45 ft high. $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. How high does it go? $301.0$ ft

Find when it lands
A baseball is hit straight up at 80 ft/s from 25 ft above the field. $h (t) = - 16 t^{2} + 80 t + 25$ gives the height in feet $t$ seconds after launch. When does it hit the field? $5.3$ s
In a physics lab, an arrow is shot straight up; $h (t) = - 16 t^{2} + 96 t + 55$ gives the height in feet $t$ seconds after launch. How many seconds after launch does it land? $6.5$ s
For a ball thrown straight up, $h (t) = - 16 t^{2} + 128 t + 45$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land? $8.3$ s
In a physics lab, a rocket is fired straight up; $h (t) = - 16 t^{2} + 96 t + 60$ gives the height in feet $t$ seconds after launch. After how long, to the nearest tenth of a second, does it land? $6.6$ s
For an arrow shot straight up, $h (t) = - 16 t^{2} + 88 t + 15$ gives the height in feet $t$ seconds after launch. When does it land? $5.7$ s

Write parametric equations for a launch
A ball is hit at 64 ft/s at $60^{\circ}$ from 2 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 32 t$ ,
$y = - 16 t^{2} + 32 \sqrt{3} t + 2$ ;
about 112.0 ft
An arrow is shot at 70 ft/s at $60^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 35 t$ ,
$y = - 16 t^{2} + 35 \sqrt{3} t$ ;
about 132.6 ft
A ball is thrown at 114 ft/s at $45^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 57 \sqrt{2} t$ ,
$y = - 16 t^{2} + 57 \sqrt{2} t + 5$ ;
about 411.1 ft
A ball is thrown at 48 ft/s at $30^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 24 \sqrt{3} t$ ,
$y = - 16 t^{2} + 24 t$ ;
about 62.4 ft
A soccer ball is kicked at 90 ft/s at $30^{\circ}$ from 5 ft above the ground. Write parametric equations and find how far it travels horizontally, to the nearest tenth. $x = 45 \sqrt{3} t$ ,
$y = - 16 t^{2} + 45 t + 5$ ;
about 227.6 ft

Find when it reaches a given height
$h (t) = - 16 t^{2} + 112 t + 25$ . When is the object 217 ft high? $t = 3$ s and $t = 4$ s
$h (t) = - 16 t^{2} + 96 t$ . When is the object 80 ft high? $t = 1$ s and $t = 5$ s
$h (t) = - 16 t^{2} + 96 t + 24$ . When is the object 152 ft high? $t = 2$ s and $t = 4$ s
$h (t) = - 16 t^{2} + 112 t$ . When is the object 160 ft high? $t = 2$ s and $t = 5$ s
$h (t) = - 16 t^{2} + 80 t + 17$ . When is the object 113 ft high? $t = 2$ s and $t = 3$ s

How to do these

$h (t) = - 16 t^{2} + 64 t + 10$ . When is the object 58 ft high?

Set h(t) = 58 and move 58 over: -16t² + 64t - 48 = 0.
Divide by -16: t² - 4t + 3 = 0, so (t - 1)(t - 3) = 0.
Once on the way up, once on the way down.

The answer is $t = 1$ s and $t = 3$ s.

Where students go wrong

Keeping the negative root when finding when it lands. The quadratic formula usually gives one negative time, and the object was not in the air before it was launched, so only the positive answer counts.

Also called height of a projectile, maximum height, quadratic word problems or falling objects.

What you can put on this worksheet

The greatest height: A flare is fired upward at 48 ft/s from a platform 24 ft up. $h (t) = - 16 t^{2} + 48 t + 24$ gives the height in feet $t$ seconds after launch. Find the greatest height. → $60.0$ ft
When it is highest: A flare is fired upward at 48 ft/s from a platform 24 ft up. $h (t) = - 16 t^{2} + 48 t + 24$ gives the height in feet $t$ seconds after launch. When does it reach its greatest height? → $1.5$ s
When it lands: A flare is fired upward at 48 ft/s from a platform 24 ft up. $h (t) = - 16 t^{2} + 48 t + 24$ gives the height in feet $t$ seconds after launch. When does it hit the ground? → $3.4$ s
Launched at an angle: A ball is hit at 84 ft/s at $45^{\circ}$ from ground level. Write parametric equations and find how far it travels horizontally, to the nearest tenth. → $x = 42 \sqrt{2} t$ ,
$y = - 16 t^{2} + 42 \sqrt{2} t$ ;
about 220.5 ft
When it is at a given height: $h (t) = - 16 t^{2} + 112 t + 22$ . When is the object 182 ft high? → $t = 2$ s and $t = 5$ s
In meters: A ball is kicked at 12 m/s at $40^{\circ}$ from 1 m above the ground. Write parametric equations $(g = 9.8 {m/s}^{2})$ and find how far it travels, to the nearest tenth of a meter. → $x = 12 \cos 40^{\circ} t$ ,
$y = - 4.9 t^{2} + 12 \sin 40^{\circ} t + 1$ ;
about 15.6 m
Time, distance, highest point: A ball is hit at 88 ft/s at $45^{\circ}$ from 6 ft above the ground $(g = 32 {ft/s}^{2})$ . To the nearest tenth, find the time in the air, the horizontal distance, the time of the greatest height, and the greatest height. → $4.0 s,$ $247.9 ft,$ $1.9 s,$ $66.5 ft$
Sketch the path: A ball is launched from the ground at 64 ft/s at $45^{\circ} (g = 32 {ft/s}^{2})$ . Sketch its path and give the horizontal distance and the greatest height, to the nearest tenth. → Distance $128.0 ft$ ; greatest height $32.0 ft$

Questions about these worksheets

Yes. Every projectile motion sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the projectile motion questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 8: the greatest height, when it is highest, when it lands, launched at an angle, when it is at a given height, in meters, time, distance, highest point and sketch the path. Tick as many as you want and set how many of each, or let it spread them evenly.

Answering the wrong question. The time at the top and the height at the top are different numbers, and so is the time it lands. Read which one is asked for before doing anything.

Projectile motion worksheet for Algebra 2

Select your difficulty

Find the greatest height

Find when it lands

Write parametric equations for a launch

Find when it reaches a given height

Find the greatest height

Find when it lands

Write parametric equations for a launch

Find when it reaches a given height

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these projectile motion worksheets free?+

Do the projectile motion worksheets come with an answer key?+

Are these projectile motion worksheets printable?+

What grade are these projectile motion worksheets for?+

Can I get a different version of the same projectile motion worksheet?+

Is this a free alternative to Kuta Software for projectile motion?+

Can I choose how hard the projectile motion questions are?+

What kinds of question are on a projectile motion worksheet?+

What do students get wrong with projectile motion?+