Question

From the top of a tower, two stones, whose masses are in the ratio $1:2$are thrown on straight up with an initial speed $u$ and the second straight down with the same speed $u$. Then, neglecting air resistance

• A. the heavier stone hits the ground with a higher speed
• B. the lighter stone hits the ground with a higher speed
• C. both the stones will have the same speed when they hit the ground
• D. the speed cannot be determined with the given data

Answer 1

The correct option is C

both the stones will have the same speed when they hit the ground

Free fall:

1. In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it.
2. Here, the only force acting on two bodies of different masses is due to gravity, and both have the same initial velocity $u$
3. The first stone is thrown straight up with velocity $u$ upward and the acceleration due to gravity acts downwards.
4. So the First particle goes up to some height until its velocity becomes zero and then this particle falls freely. Now when the particle reaches the level of the top of the tower its velocity becomes $u$ downward and acceleration due to gravity is also in the downward direction.
   
5. By using newtons law of motion. for the first particle, the final velocity on reaching the ground is $v=\sqrt{u^2+2gh}$ ,where $h$ is the height of the tower and$g$ is the acceleration due to gravity
6. For the second body, with an initial velocity $u$ and gravity acting in the downward direction, its final velocity on reaching the ground is $v=\sqrt{u^2+2gh}$

Hence, both the particle reaches the ground with the same velocity. Therefore, option C is correct