Kinematics Review

Kinematics equations/ review guideline

Chapter 3

1.         A tennis ball is dropped from 1.2m above the ground. It rebounds to a height of 1m.

a.        With what speed does it hit the ground?

d= v_i*t+1/2*a*t^2→1.2=0*t+1/2*9.8*t^2→4.9t^2=1.2→t^2=2.4→t=1.55s

v_f=v_i+a*t→ v_f=0+9.8*1.55=15.19m/s 

b.        With what speed does it leave the ground?

v_f^2=v_i^2+2*a*d→0= v_i^2+2*-9.8*1→v_i^2=19.6=4.4m/s

2.         A car starts from rest and gets to a store that is 400m away. The car’s velocity when it gets to the store is 10m/s.  Another car that starts in the same place, is already moving at 12m/s. Which car is going to get to the store first and by how many seconds less will it travel?

CAR 1: d=(v_i+v_f)/2*t→400=(0+10)/2*t→400=5t→t=80s

CAR 2: d=(v_i+v_f)/2*t→400=12t→33.3s

CAR 2 will get to the store 46.66s before the CAR 1

3.         Engineers are developing new types of guns that might someday be used to launch satellites as if they were bullets. One such gun can give a small object a velocity of 1m/s moving it through only 2cm.

a.        What acceleration does the gun give this object?

d=(v_i+v_f)/2*t→.02=(0+1)/2*t→t=.04s 

v_f=v_i+a*t→1=0+a*.04→1=.04a→a=25m/s 

b.        Over what time interval does the acceleration take place?

d=(v_i+v_f)/2*t→.02=(0+1)/2*t→t=.04s 

4.         A rock is thrown down into a well with an initial downward speed of 3m/s. The rock hits the bottom 1.8s later.

a.        How deep is the well?

v_f=v_i+a*t→v_f=3+9.8*1.8→v_f=20.64m/s 

d=(v_i+v_f)/2*t→d=(3+20.64)/2*1.8→d=21.276m 

b.        What is the rock's speed as it hits the bottom?

v_f=v_i+a*t→v_f=3+9.8*1.8→v_f=20.64m/s 

5.         A hot air balloon is ascending at a steady velocity of 2.2m/s. An object is dropped from it.  What is the distance from the object and the balloon after 0.5s?

d= v_i*t+1/2*a*t^2→d=2.2*.5+1/2*9.8*〖.5〗^2→d=2.325m