Question

One stone is projected horizontally from a 20 m high cliff with an initial speed of 10ms⁻¹. A second stone is simultaneously dropped from that cliff. Which of the following is true?
A) Both strike the ground with the same velocity.
B) The ball with initial speed 10m/s strikes the ground first.
C) Both the balls hit the ground at the same time.
D) One cannot say without knowing the height of the building.

Answer 1

Hint: In this question both the stones have to travel the same vertical distance, and the initial velocity of both the stones is zero in the vertical direction and hence by calculating the time we can come to a conclusion.

Complete step by step answer:
Given:
The height of the cliff is H=20m.
The initial velocity of the second stone, which is vertically dropped is U=0.
We can say that the vertical component of the initial velocity of horizontal projected first stone is V=0 m/s.
We know that the time taken by both the stones is given by: $T = \sqrt {\dfrac{{2H}}{g}} $ and $t = \sqrt {\dfrac{{2H}}{g}} $
Here T and t are the time taken by the first and second stone to reach the ground and g is the acceleration due to gravity.
In the above equation, H=20 m is the same for both cases. Therefore, we can say that:
$ \Rightarrow T = t$

Therefore, both stones will reach the ground at the same time, and the correct option is (C).

Additional information: When a stone is dropped from a height, it falls towards the earth. This event proves that there must be a force in a downward direction which causes this motion. It is nothing but the weight which causes this motion. The weight is a force by which earth is attracted toward the earth, or the stone is attracted towards the earth. This is according to Newton’s third law of motion, which states that to every action, there is an equal and opposite reaction. Hence the force of attraction of stone towards earth is the same as the force of attraction of earth towards the stone. This force of attraction has a value called the weight of the stone.

Note: If an object falls from a height and it is falling only under gravity, and no external forces are applied then this is the condition of the free fall, and in this condition, the initial velocity of the object will be taken zero while if an object is thrown vertically downward with some force, then its initial velocity will not be considered zero.