THESE TIMES ARE EQUAL The time it takes for that object to hit the ground if I just drop it.

v

iy = 0 The time it takes for an object thrown horizontally to hit the ground

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: #1

Tom 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 v x . Find an equation with this, and see what I’m missing.

d y



v t iy



1 2

gt

2

d y



1 2

gt

2 It takes the same amount of time to hit the ground if I

throw it horizontally

does if

I simply drop it

… i.e.,

v

i as it = 0

v x



d x t

 45.0

t

I need

t

t



2

d y g



v x



45 2.86



15.7

9.8



2.86

s

Each dot = ½ second

WORKSHEET 1: #2

Erica 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?

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

d y



v t iy

 1 2

gt

2

d y

 1 2

gt

2  1 2

I need

t

d y

 1  2

t

2

v x



d x t t



d x v x

 15.0

3.80

 3.95

s

 2  76.5

m

It takes the same amount of time to hit the ground if I

throw it horizontally

does if

I simply drop it

… i.e.,

v

i as it = 0

Each dot = ½ second

WORKSHEET 1: #3

Kelly 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: #4

Thelma 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

WORKSHEET 1: #5

Elaine shoots a bullet straight up in the air from a gun. It reaches a height of 1940 m. How fast was the bullet fired?

I need v iy . Find an equation with this, and see what I’m missing.

v

2

fy



v

2

iy

 2

gd

0 

v iy

2  2

gd v iy

 2

gd

 

 

At the highest point, the object momentarily stops, i.e.,

v

f = 0

Each dot = 1 second

WORKSHEET 1: #6

How long is the bullet in #5 in the air before it hits the ground again?

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

t

 2

v iy g

 9.81



39.8

s

19.9 seconds

(red dots)

going up, and 19.0 seconds coming down.

Each dot = 1 second

WORKSHEET 1: #7

If 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: #1

Chris 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?

NOTE: With projectiles above the horizontal, I would calculate both vectors first, and label them.

v x v y

 

   

 

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

t

 2

v iy g

 9.81



2.76

s



Each dot = 0.25 seconds

WORKSHEET 2: #2

What is the maximum height for the rock in #1?

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

v

2

fy



v iy

2  2

gd

0 

v iy

2  2

gd d

 

v iy

2  2

g



 13.5

  

2 2 9.81





9.30

m

At the highest point, the velocity in the

y

direction = 0;

v

yf = 0

Each dot = 0.25 seconds

WORKSHEET 2: #3

How far away did the rock in #1 land?

I need d

x

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

v x



d x t d x

 

v t x

 

s

  44.4

m

Each dot = 0.25 seconds

WORKSHEET 2: #4

Nicole 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: #5

Jason 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: #6

An 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: #7

Alex 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?

NOTE: With projectiles above the horizontal, I would calculate both vectors first, and label them.

v x



v y



 

 

I need d

x

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

d y

  1 2

gt

2 

t



v x



d x t

4.9

t

2  12.8

t

 40  0

d x



v t x





18.5



t

I need

t

d x



t

 1.84

s

     34.0

m t

2

Each dot = 0.25 seconds

WORKSHEET 2: #8

What is the maximum range for a projectile fired with a velocity of 80 m/s?

WORKSHEET 3: #1

A 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?

NOTE: With projectiles above the horizontal, I would calculate both vectors first, and label them.

v x



v y



 

  32.2

/

I need d

y

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

d y



v t iy

 1 2

gt

2 





16.8

m

  

2 

 

2 if we’re calling velocity UP as positive; Then gravity, pulling DOWN, must be negative.

Each dot = 1 second

WORKSHEET 3: #2

A 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?

v x v y

        14.4

/ 17.2

/

I need d

y

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

d y



v t iy

 1 2

gt

2

v x



d x t d y

  17.2

 1 2   9.81

  2

t



d x v x

 45.7

14.4

 3.17

s

I need

t

d y

     1 2     2  5.28

m

Each dot = 0.1 seconds

WORKSHEET 3: #3

A 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.

v

 30

v x

65   12.7

v x

 12.7

Remember .. In the horizontal direction, velocity is constant

15

?

v f

I need

v

f

a

 

v t



v f t



v i t



v f



g v i v

2

f

 12.7

2  15 2

t



v f

 27.2

 9.8

t

   

9.8

v

2

f

  63.71

v f

 7.98

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



3.59

s

t = 3.59 seconds …

We are right!

WORKSHEET 3: #4

A 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? tan

v yf

110

v

2

yf



v

2

yi



2

ad

   tan  1  

v yf

110  

I need

v

f

v yf

  161    tan  1 161 110  55.7

 

 

200 56.7° 110 167

 

110

v yf

 ?

If I knew v yf, I could find the angle by using inverse tangent.

Remember .. In the horizontal direction, velocity is constant

Each dot = 0.1 seconds

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?

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

d y



v t iy v x



d x t d x



v t x at

2  

t

  9.8



t

2  4.9

t

2  10

t

 50  0

Use quadratic formula to solve for t.

t

 4.37

s

I need

t

d x

    

75.6

m

Each dot = 0.25 seconds