Question

Rahman drops two stones P and Q each of mass 1 kg and 2 kg simultaneously from
the top of a tower of height 20 m. Both start from rest and fall freely downwards. Find
the time taken by the stone P to reach the ground. Does the stone Q reach the ground at
the same time? Find the velocity of the stone Q with which it hits the ground.
(Take g = 10 m/s2
)

Answer 1

This question involves the use of the equations of motion for vertical motion.

The time taken by the stones P and Q to reach the ground is the same, that is "2 s".

The velocity with which Q hits the ground is "20 m/s".

The time taken by the stones to reach the ground can be calculated by using the second equation of motion for the vertical motion:

$h = v_it+\frac{1}{2}gt^2$

For both the stones P and Q:

h = height = 20 m

$v_i$ = initial velocity = 0 m/s

t = time = ?

g = acceleration due to gravity = 10 m/s²

Therefore,

$20\ m = (0\ m/s)t+\frac{1}{2}(10\ m/s^2)(t)^2\\\\t = \sqrt{\frac{20\ m}{5\ m/s^2}}$

t = 2 s

Hence, the time taken by both the stones to reach the ground is the same.

To find the final velocity of stone Q we will use the first equation of motion for the vertical motion:

$v_f=v_i+gt\\v_f = 0\ m/s+(10\ m/s^2)(2\ s)\\v_f = 20\ m/s$

Learn more about equations of motion here:

brainly.com/question/20594939?referrer=searchResults

The attached picture shows the equations of motion in the horizontal and vertical directions.