Step-by-step explanation:
The increase in kinetic energy of a body when it falls from a height can be calculated using the following formula:
\[ \text{Increase in Kinetic Energy} = \text{Final Kinetic Energy} - \text{Initial Kinetic Energy} \]
The initial kinetic energy (\(KE_{\text{initial}}\)) of the body is zero because it's initially at rest. The final kinetic energy (\(KE_{\text{final}}\)) can be calculated using the formula:
\[ KE_{\text{final}} = \frac{1}{2} \cdot m \cdot v^2 \]
Where:
- \( m \) is the mass of the body (100 kg).
- \( v \) is the final velocity of the body when it hits the ground.
To find \( v \), you can use the following kinematic equation:
\[ v^2 = u^2 + 2as \]
Where:
- \( u \) is the initial velocity (which is 0 m/s because the body starts from rest).
- \( a \) is the acceleration due to gravity (approximately 9.81 m/s², assuming standard Earth gravity).
- \( s \) is the height from which the body falls (10 m).
Plugging in the values:
\[ v^2 = 0^2 + 2 \cdot 9.81 \cdot 10 \]
\[ v^2 = 196.2 \]
\[ v ≈ 14.0 \, \text{m/s} \]
Now, calculate the final kinetic energy:
\[ KE_{\text{final}} = \frac{1}{2} \cdot 100 \, \text{kg} \cdot (14.0 \, \text{m/s})^2 \]
\[ KE_{\text{final}} ≈ 9800 \, \text{Joules} \]
Now, calculate the increase in kinetic energy:
\[ \text{Increase in Kinetic Energy} = KE_{\text{final}} - KE_{\text{initial}} = 9800 \, \text{Joules} - 0 \, \text{Joules} \]
So, the increase in kinetic energy of the body is 9800 Joules.