Section 2.27  Sample problem: free fall  
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The ball is thrown straight up, with velocity 10.0 m/s.

When will its velocity be −5.60 m/s?
 

As you see above, a ball is tossed straight up into the air with an initial velocity of positive 10.0 meters per second. You are asked to figure out how long it will take before its velocity is negative 5.60 m/s. The ball will have this velocity when it is falling back to the ground.

Draw a diagram

Variables

Be careful with the signs for acceleration and velocity. We use the common convention that upward quantities are positive, and downward negative. The magnitude of the acceleration is the free-fall acceleration constant g = 9.80 m/s2.

 

initial velocity

vi = 10.0 m/s

 

final velocity

vf = −5.60 m/s

 

acceleration

a = −9.80 m/s2

 

elapsed time

t

What is the strategy?

  1. Choose an appropriate motion equation for the knowns and unknowns.
  2. Solve for the elapsed time.

Physics principles and equations

This motion equation involves just the values we know and the time we want to find.

vf = vi + at

Step-by-step solution

 

  
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