If a body of mass 4 kg is lifted to a height of 10 m and then released, what will be the velocity of the body when it strikes the ground?

Options:
1. 10 m/s
2. 20 m/s
3. 14 m/s
4. 28 m/s

The velocity of the body when it strikes the ground, after being lifted to a height of 10 m, is approximately 14 m/s. This is calculated using the energy conservation principle where gravitational potential energy converts to kinetic energy. Hence, the chosen option is 3: 14 m/s.
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Answered by Anonymous | 2025-07-04

To solve this problem, we can use the principle of conservation of energy, this states that the total energy in a system remains constant if only conservative forces, like gravity, act on it.
When the body is lifted to a height, it has potential energy and no kinetic energy. As it is released and falls, the potential energy is converted into kinetic energy.
The potential energy at the height h is given by: PE = m ⋅ g ⋅ h where:

m = 4 kg (mass of the body)
g = 9.8 m/s 2 (acceleration due to gravity)
h = 10 m (height)

So, the potential energy at the top is: PE = 4 ⋅ 9.8 ⋅ 10 = 392 J (joules)
At the moment it strikes the ground, all potential energy has been converted to kinetic energy ( K E ). The kinetic energy is given by: K E = 2 1 ​ m v 2 where v is the velocity of the body.
Setting the kinetic energy equal to the potential energy, we get: 2 1 ​ ⋅ 4 ⋅ v 2 = 392
Solving for v , 2 ⋅ v 2 = 392 v 2 = 196 v = 196 ​ v = 14 m/s
Therefore, the velocity of the body when it strikes the ground is 14 m/s. The correct option is 3: 14 m/s.

Answered by SophiaElizab | 2025-07-06