A body is thrown up with a velocity of 100m/s if it travels 5 m in the last seconds of its journey . If the same ball is thrown up with the initial velocity of

Question

A body is thrown up with a velocity of 100m/s if it travels 5 m in the last seconds of its journey . If the same ball is thrown up with the initial velocity of 200m/s . What distance will it travel in the last two second of its journey?

Answer 1

A ball with initial velocity 100m/s will reach a maximum height s = (v²_{f -} v²_i) / 2g = 100² / 2(10) = 500m

The time to travel back to the ground is 10 seconds

In the first 8 seconds it travels 320m,

therefore in the final 2 seconds it travels 180m

 

Similarly a ball with initial velocity 200m/s will reach maximum height 2000m

The time to travel back to the ground is 20 seconds

In the first 18 minutes it travels 1620m.

therefore on the final 2 seconds it travels 380m.

 

There is an inconsistency because the question says the ball with velocity 100m/s travels 5m in the last 2 seconds but physics says 180m so perhaps air resistance is a factor

 

 

 

 

 

Answer 2

Assuming that the the 5 m travel mentioned is in the last TWO seconds of its travel, and that the end of travel means the the part just before reaching the maximum height,  the answer is that there is no difference between the ball thrown at 100 m/s and the one one thrown at 200 m/s.

 

A way of seeing this is to remember that the distance traveled in the last two seconds of travel is the same as the distance downward that will be traveled in two seconds after the ball reaches its maximum height.  This distance is 0.5 g 2² .