Question

A $600\, kg$ rocket is set for a vertical fring. If the exhaust speed is $1000 \,ms^{-1}$ the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is

• A. $ 117.6\, kgs^{-1}$
• B. $ 58.6 \,kgs^{-1}$
• C. $6\, kgs^{-1}$
• D. $ 76.4\, kgs^{-1}$

Answer 1

The Correct Option is C

To solve this problem, we'll need to calculate the mass of the gas ejected per second to provide a thrust that can overcome the weight of the rocket.

Let's break down the problem step-by-step:

1. Weight of the Rocket: W = mg, where m = 600\, \text{kg} and g = 9.8\, \text{m/s}^2 (acceleration due to gravity).
   W = 600 \times 9.8 = 5880\, \text{N} (Newtons)
2. Thrust Requirement: The thrust provided by the ejected gas must be equal to the weight of the rocket in order to overcome gravity.
   Therefore, F = 5880\, \text{N}.
3. Thrust Equation: The thrust F produced by the ejected gas is given by F = v \cdot \dot{m}, where v = 1000\, \text{m/s} is the exhaust speed and \dot{m} is the mass of gas ejected per second.
4. Calculate Mass Ejection Rate: We have F = v \cdot \dot{m}. Substituting the known values, we get: 5880 = 1000 \cdot \dot{m}.
   Solving for \dot{m}, we get: \dot{m} = \frac{5880}{1000} = 5.88\, \text{kg/s}.
   However, the closest option that matches this value is 6\, \text{kg/s}.

Thus, the mass of the gas ejected per second to overcome the weight of the rocket is approximately 6\, \text{kg/s}.