A body dropped from a height $h$ with an initial speed of zero, strikes the ground with a velocity $3 ext{ k

Question

A body dropped from a height $h$ with an initial speed of zero, strikes the ground with a velocity $3 	ext{ km/h}$. Another body of the same mass is dropped from the same height $h$ with an initial speed $u' = 4 	ext{ km/h}$. Find the final velocity of the second body with which it strikes the ground.

Accepted Answer

1. **Analyze First Body:** The body falls from height $h$ starting from rest ($u_1 = 0$).
   - Using the kinematic equation $v^2 = u^2 + 2as$ with $a=g$ and $s=h$:
   $$ v_1^2 = u_1^2 + 2gh $$
   $$ (3)^2 = 0^2 + 2gh \implies 2gh = 9 $$
2. **Analyze Second Body:** The second body falls from the same height $h$ but with an initial velocity $u_2 = 4 	ext{ km/h}$. The mass of the body does not affect the final velocity in free fall (neglecting air resistance).
   - Using the same kinematic equation for the final velocity $v_2$:
   $$ v_2^2 = u_2^2 + 2gh $$
   - Substitute the known values ($u_2 = 4$ and $2gh = 9$):
   $$ v_2^2 = (4)^2 + 9 $$
   $$ v_2^2 = 16 + 9 = 25 $$
   $$ v_2 = \sqrt{25} = 5 	ext{ km/h} $$ .

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