Physics 2001 JAMB Past Questions - Question 3: A stone of mass 1 kg is dropped from a height of 10m above the ground and falls freely under gravity. Its kinetic energy 5m above the ground is then equal to

Correct Answer

D

Explanation

To find the kinetic energy of the stone when it is 5 meters above the ground, you can use the following formula:

Kinetic Energy (KE) = 1/2 * m * v^2

Where:
KE is the kinetic energy,
m is the mass of the stone (1 kg in this case),
v is the velocity of the stone.

To find the velocity of the stone when it's 5 meters above the ground, you can use the following equation of motion for freely falling objects:

h = (1/2) * g * t^2

Where:
h is the height (5 meters in this case),
g is the acceleration due to gravity (approximately 9.81 m/s^2),
t is the time taken.

First, we need to find the time it takes for the stone to fall 5 meters:

5 = (1/2) * 9.81 * t^2

Solving for t:

t^2 = (2 * 5) / 9.81
t^2 = 10 / 9.81
t ≈ √(10 / 9.81)
t ≈ 1.43 seconds

Now that we have the time, we can find the velocity of the stone when it's 5 meters above the ground using the equation:

v = g * t

v ≈ 9.81 m/s^2 * 1.43 s
v ≈ 14.03 m/s

Now, you can calculate the kinetic energy at that point:

KE = 0.5 * 1 kg * (14.03 m/s)^2
KE ≈ 98.17 joules

So, the kinetic energy of the stone when it's 5 meters above the ground is approximately 98.17 joules.