Question

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20 m/s\(^2\), the amount of gas ejected per second to supply the needed thrust will be (Take \(g = 10 \, \text{m/s}^2\))

• A. 127.5 kg/s
• B. 137.5 kg/s
• C. 155.5 kg/s
• D. 187.5 kg/s

Hint:

To calculate the required mass flow rate for rocket thrust, use the formula \( \dot{m} = \frac{F}{v} \), where \( F \) is the thrust and \( v \) is the exhaust velocity.

Answer 1

The Correct Option is B

Step 1: Calculate the force needed for the upward acceleration.
Using Newton's second law \( F = ma \), where \( m = 5000 \, \text{kg} \) and \( a = 20 \, \text{m/s}^2 \), we get: \[ F = 5000 \times 20 = 100000 \, \text{N} \]
Step 2: Calculate the rate of gas ejection.
The thrust required is provided by the rate of gas ejection \( \dot{m} \) and the exhaust velocity \( v = 800 \, \text{m/s} \). From the equation for thrust \( F = \dot{m} v \), we get: \[ \dot{m} = \frac{F}{v} = \frac{100000}{800} = 137.5 \, \text{kg/s} \]
Final Answer: \[ \boxed{137.5 \, \text{kg/s}} \]