Question

Two stones of different masses are thrown vertically upward with the same initial velocity. Which one will rise to a greater height?

Answer 1

Free fall and motion:

The displacement of two stones thrown vertically upwards, of falling freely from a certain height does not depend upon its masses.

Step 1: Calculation of time

1. Velocity can be defined as the rate of change of position of a body with respect to time.
2. The final velocity of an object can be expressed as follows:

$\mathrm{v}=\mathrm{u}+\mathrm{at}$

Here, $\mathrm{v}$ is the final velocity, $\mathrm{u}$ is the initial velocity, and $\mathrm{t}$ is the time.

3. At the maximum position, the initial velocity will be zero for both stones.

4. For vertically thrown objects, the acceleration is the same and equal to the acceleration due to gravity.

5. Since the initial velocity for both stones is the same, the time for both stones will be the same.

Step 2: Calculation of displacement

Displacement can be calculated as follows:

$s=ut+\frac{1}{2}a{t}^2$

Here, $s$ is the displacement.

Since all the variables for both stones are the same, the displacement of both is also the same.

Hence, the two stones will rise up to the same height.