Question

A rock of mass 5kg and another of mass 10kg are dropped at the same instant from a tower of height 100m. Find the ratio of their velocities just before hitting the ground ​

Answer 1

Answer:

The ratio is 1:1.

Explanation:

According to the following equation:

       $v=\sqrt{u^2+2as}$

we know that the velocity of an object depends on its initial velocity, acceleration, and the distance traveled.

• For both rocks, the initial velocity $u$ is same, which is 0 m/s (since they are being "dropped" not "thrown".
• For both rocks, the acceleration is same, since the only acceleration is due to gravity (9.8 m/s²)
• For both rocks, the distance traveled is same, since they are being dropped from the same tower.

This means that the final velocities of BOTH the rocks will be exactly the same! Hence, the ratio of the final velocity will be 1:1.

The above sentence can be expressed mathematically. Assume $v_1$ as final velocity of first rock, $v_2$ as final velocity of second rock. We need to find $\frac{v_1}{v_2}$:

       $\dfrac{v1}{v2} = \dfrac{\sqrt{u^2+2as}}{\sqrt{u^2+2as}}=\dfrac{1}{1}$

       $\therefore v_1:v_2=1:1$

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