THESE TIMES ARE

EQUAL

The time it takes for an object thrown

horizontally to hit the ground

The time it takes for that object to hit the ground if I just drop

it.

viy = 0

Look how gravity affects vertical motion

… the distance gets bigger.

Horizontal velocity is constant …

Always use this formula

For the horizontal part, gravity plays no role. The distance

between points is always the same.

WORKSHEET 1: #1Tom throws a rock horizontally off of a 40.0 m high cliff. How fast did he throw the rock if it hits the ground 45.0 m from

the base of the cliff?

I need vx. Find an equation with this, and see what I’m

missing.

45.0xx

dv

t t

21

2y iyd v t gt

21

2yd gt

2 2 402.86

9.8ydt sg

4515.7 /

2.86xv m s

It takes the same amount of time to hit the ground if I throw it horizontally as it does if I simply drop it … i.e., vi = 0

I need

t

Each dot = ½ second

WORKSHEET 1: #2Erica throws a ball out of a window with a horizontal speed of 3.80 m/s.

If the ball hit the ground 15.0 m away, how high up is the window?

21

2y iyd v t gt

2 21 19.8

2 2yd gt t

I need

t

Each dot = ½ second

xx

dv

t

15.03.95

3.80x

x

dt sv

219.81 3.95 76.5

2yd m

I need dy. Find an equation with this, and see what I’m

missing.

It takes the same amount of time to hit the ground if I throw it horizontally as it does if I simply drop it … i.e., vi = 0

WORKSHEET 1: #3Kelly shoots a rock in a sling shot

horizontally at 12.5 m/s from the top of a 30.0 m high building. How far from the base of the building does the rock hit?

Each dot = ½ second

WORKSHEET 1: #4Thelma drives her car off a cliff 60.0 m

high. It hits the ground 125 m out horizontally from the bottom of the cliff.

How fast was she driving?

Each dot = ½ second

Each dot = 1 second

WORKSHEET 1: #5Elaine shoots a bullet straight up in the

air from a gun. It reaches a height of 1940 m. How fast was the bullet fired?

2 2 2fy iyv v gd

20 2iyv gd

2iyv gd

2 9.81 1940

195 /m s

I need viy. Find an equation with this, and see what I’m

missing.

At the highest point, the object momentarily stops, i.e., vf = 0

WORKSHEET 1: #6How long is the bullet in #5 in the air

before it hits the ground again?

2 iyvtg

2 195

9.81

39.8s

I need t. Find an equation with this, and see what I’m

missing.

Each dot = 1 second

19.9 seconds (red dots) going up, and 19.0

seconds coming down.

WORKSHEET 1: #7If Elaine had shot the bullet from #5

horizontally from a height of 2.50 m, how far would the bullet have gone before

hitting the ground?

Each dot = 0.1 seconds

WORKSHEET 2: #1Chris throws a rock at 21.0 m/s into the air at 40.0°

above the horizontal. How long is the rock in the air?

Each dot = 0.25 seconds

21cos 40 16.1 /

21sin 40 13.5 /

x

y

v m s

v m s

I need t. Find an equation with this, and see what I’m

missing.

2 iyvtg

2 13.5

9.81

2.76s

NOTE:With projectiles above the horizontal, I would

calculate both vectors first, and label them.

WORKSHEET 2: #2What is the maximum height for the rock

in #1?

I need d. Find an equation with this, and see what I’m

missing.

2

2iyvdg

2 2 2fy iyv v gd

20 2iyv gd

213.5

2 9.81

9.30m

Each dot = 0.25 seconds

At the highest point, the velocity in the y direction = 0;

vyf = 0

WORKSHEET 2: #3How far away did the rock in #1 land?

x xd v t 16.1 2.76 44.4s m

xx

dv

t

I need dx. Find an equation with this, and see what I’m

missing.

Each dot = 0.25 seconds

WORKSHEET 2: #4Nicole throws a ball at 25.0 m/s at an

angle of 63.8° above the horizontal. What was the range of the ball?

Each dot = 0.25 seconds

WORKSHEET 2: #5Jason throws a ball at 25.0 m/s at an

angle of 26.2º above the horizontal. What is the range of the ball?

Each dot = 0.25 seconds

WORKSHEET 2: #6An airplane flying at 450 km/hr and 3330 m above the ground drops a bomb on a target. How far in front of the target will the plane have to release the bomb in order to hit it?

Each dot = 1 second

WORKSHEET 2: #7Alex throws a ball at 22.5 m/s at an angle of 34.8° below the horizontal from the top of a 40.0 m high

building. How far from the base of the building does the ball hit?

Each dot = 0.25 seconds

I need dx. Find an equation with this, and see what I’m

missing.

22.5cos 34.8 18.5 /

22.5sin 34.8 12.8 /

x

y

v m s

v m s

xx

dv

t

18.5x xd v t t

I need

t

21

2y iyd v t gt

240 12.8 .5 9.8t t

24.9 12.8 40 0t t

1.84t s

18.5 1.84 34.0x xd v t m

NOTE:With projectiles above the horizontal, I would

calculate both vectors first, and label them.

WORKSHEET 2: #8What is the maximum range for a

projectile fired with a velocity of 80 m/s?

WORKSHEET 3: #1A ball is thrown at 33.3 m/s at an angle of 75.5º from the ground. How high off the ground is the

ball after 6.00 s?

Each dot = 1 second

33.3cos 75.5 8.3 /

33.3sin 75.5 32.2 /

x

y

v m s

v m s

I need dy. Find an equation with this, and see what I’m

missing.

21

2y iyd v t gt

2132.2 6 9.81 6

2

16.8m

if we’re calling velocity UP as

positive;

Then gravity, pulling DOWN,

must be negative.

NOTE:With projectiles above the horizontal, I would

calculate both vectors first, and label them.

WORKSHEET 3: #2A kicker wants to kick a 45.7 m (50 yd) field goal.

The crossbar of the upright is 3.05 m above the ground. The kicker can kick with a velocity of

22.4 m/s. The ball is kicked at an angle of 50.0° above the ground. If the ball is kicked straight, is

the field goal good?

Each dot = 0.1 seconds

22.4cos 50 14.4 /

22.4sin 50 17.2 /

x

y

v m s

v m s

21

2y iyd v t gt

2117.2 9.81

2yd t t

I need

t

xx

dv

t

45.73.17

14.4x

x

dt sv

2117.2 3.17 9.81 3.17 5.28

2yd m

I need dy. Find an equation with this, and see what I’m

missing.

15

12.7xv

30v 2

7.2

yv

65

fv

12.7xv

?

2 2 212.7 15fv

2 225 161.29 63.71fv

7.98fv

f iv vva

t t

f iv vt

g

27.2

9.8fvt

7.98 27.23.59

9.8t s

Remember .. In the horizontal direction, velocity is constant

(Since velocity is going down in direction, it is negative.)

WORKSHEET 3: #3A ball is kicked at 30.0 m/s at an angle of 65.0º

above the ground. How long has the ball been in the air when the velocity of the ball is pointing down

and has a magnitude of 15.0 m/s?

I need t. Find an equation with t in it, and see what I’m

missing.

I need

vf

t = 3.59 seconds … We are right!

WORKSHEET 3: #4A bullet is fired at 200. m/s at an angle of 56.7°. At what angle is the bullet moving

when it is 100. m above the ground?

Each dot = 0.1 seconds

200167

11056.7°

110

?yfv

Remember .. In the horizontal direction, velocity is constant

tan110yfv

1tan110yfv

2 2 2yf yiv v ad

2167 2 9.8 100yfv

161

1 161tan 55.7

110

I need

vf

If I knew vyf, I could find the angle by using

inverse tangent.

WORKSHEET 3: #5

Jane is standing on top of a 50.0 m high building.

She throws a ball at 20.0 m/s at an angle of 30.0º

above the horizontal. If she was standing on the edge

of the building when she threw the ball, how far from

the base of the building does the ball hit the ground?

Each dot = 0.25 seconds

I need dx. Find an equation with in it, and see what I’m missing.

x xd v t

xx

dv

t

I need

t

21

2y iyd v t at

250 10 .5 9.8t t

24.9 10 50 0t t

4.37t s

17.3 4.37 75.6xd m

Use quadratic formula to solve for t.