Answer :
Hopefully it helps you please make me BRAINILINST please it took me a lot of time to solve it so please make me BRAINILINST please
Explanation:
To estimate the loss in kinetic energy when the velocity of a body is reduced from 700 m/s to 450 m/s, we can use the formula for kinetic energy:
\[ KE = \frac{1}{2}mv^2 \]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the body,
- \( v \) is the velocity of the body.
Given:
- Initial velocity, \( v_1 = 700 \) m/s
- Initial kinetic energy, \( KE_1 = 2500 \) kJ (convert to joules: \( 1 \text{ kJ} = 1000 \text{ J} \), so \( KE_1 = 2500 \times 1000 = 2,500,000 \) J)
- Final velocity, \( v_2 = 450 \) m/s
- We need to find the final kinetic energy, \( KE_2 \).
1. Calculate the initial kinetic energy \( KE_1 \):
\[ KE_1 = \frac{1}{2}mv_1^2 \]
\[ 2,500,000 = \frac{1}{2}m \times (700)^2 \]
\[ 2,500,000 = \frac{1}{2} \times m \times 490,000 \]
\[ m \approx \frac{2,500,000}{245,000} \approx 10.2 \text{ kg} \]
2. Calculate the final kinetic energy \( KE_2 \):
\[ KE_2 = \frac{1}{2}mv_2^2 \]
\[ KE_2 = \frac{1}{2} \times 10.2 \times (450)^2 \]
\[ KE_2 = \frac{1}{2} \times 10.2 \times 202,500 \]
\[ KE_2 = \frac{1}{2} \times 2,060,500 \]
\[ KE_2 = 1,030,250 \text{ J} \]
3. Calculate the loss in kinetic energy:
\[ \text{Loss in } KE = KE_1 - KE_2 \]
\[ \text{Loss in } KE = 2,500,000 - 1,030,250 \]
\[ \text{Loss in } KE = 1,469,750 \text{ J} \]
Therefore, the loss in kinetic energy when the velocity of the body is reduced from 700 m/s to 450 m/s is approximately \( 1,469,750 \) joules.