Over the Edge1-2-4 Horizontal Projectiles

A red ball rolls off the edge of a table

What does its path look like as it falls?

Parabolic path

As the red ball rolls off the edge, a greenball is dropped from rest from the same

height at the same time

Which one will hit the ground first?

They will hitat the SAME

TIME!!!

The same time?!? How?!?

vix

The red ball has an initialHORIZONTAL velocity (vix)

But does not have any initialVERTICAL velocity (viy = 0)

The green ball falls from restand has no initial

velocity IN EITHERDIRECTION!

viy and vix = 0

One Dimension at a Time

• Both balls begin with no VERTICAL VELOCITY

• Both fall the same VERTICAL DISTANCE

• This means that the time of flight IS THE SAME IN BOTH CASES

Example #1 (not in notes)• A bullet is fired horizontally from a gun that is 1.7

meters above the ground with a velocity of 55 meters per second.

• At the same time that the bullet is fired, the shooter drops an identical bullet from the same height.

• Prove that the two bullets hit the ground at the same time.

For both bullets…

vi = 0

a = -9.81 m/s2

d = -1.7 m

• An airplane making a supply drop to troops behind enemy lines is flying with a speed of 300 meters per second at an altitude of 3.0 kilometers.

– How far from the drop zone should the aircraft drop the supplies?

Need time from vertical

d = vit + ½ at2

3000 m = 0 + ½ (-9.81 m/s2)t2

t = 24.7 s

Use time in horizontal

d = vit + ½ at2

d = (300 m/s)(24.7 s) + 0

d = 7410 m

Example #2

• A stuntman jumps off the edge of a 45 meter tall building to an air mattress that has been placed on the street below at 15 meters from the edge of the building.

– What minimum initial velocity does he need in order to make it onto the air mattress?

Need time from vertical

d = vit + ½ at2

45 m = 0 + ½ (-9.81 m/s2)t2

t = 3.03 s

Use time to find v

v = d / t

v = 15 m / 3.03 s

v = 4.95 m /s

Example #3

• An astronaut on the Moon throws a wrench horizontally with a speed of 0.5 meters per second from a height of 1.5 meters. The astronaut simultaneously drops a feather from the same height. Which object will hit first? Why?

With no air resistance and identical vertical variables they hit the

ground at the same time.

Example #4