Question

Two identical stones, A and B, are thrown from a cliff from the same height and with the same initial speed. Stone A is thrown vertically upward, and stone B is thrown vertically downward. Which of the following statements best explains which stone has a larger speed just before it hits the ground, assuming no effects of air friction?
a. Both stones have the same speed; they have the same change in Ugand the same Ki
b. A, because it travels a longer path.
c. A, because it takes a longer time interval.
d. A, because it travels a longer path and takes a longer time interval.
e. B, because no work is done against gravity.

Answer 1

Answer:

b. A, because it travels a longer path.

Explanation:

• If the stone A is thrown is thrown vertically upwards and another stone is dropped down directly from the same height above the ground then the stone A will hit the ground with a higher speed because it falls down from a greater height above the earth surface.

This can be justified by the equation of motion given below:

$v^2=u^2+2\times a\times s$

where:

$v=$ final velocity

$u=$ initial velocity

$a=$ acceleration = g (here)

$s=$ displacement of the body

• Now we know that at the maximum height the speed of the object will be zero for a moment. So for both the stones A and B the initial  velocity is zero, stone B is also dropped from a height with initial velocity zero.

• Acceleration due to gravity is same for the stones so the only deciding factor that remains is s, displacement of the stones. Since stone A is thrown upwards it will attain a greater height before falling down.

Answer 2

Answer:

Option A

Explanation:

This can be explained based on the conservation of energy.

The total mechanical energy of the system remain constant in the absence of any external force. Also, the total mechanical energy of the system is the sum of the potential energy and the kinetic energy associated with the system.

In case of two stones thrown from a cliff one vertically downwards the other vertically upwards, the overall gravitational potential energy remain same for the two stones as the displacement of the stones is same.

Therefore the kinetic energy and hence the speed of the two stones should also be same in order for the mechanical energy to remain conserved.