Question

A rocket with total mass 3.00 3 105 kg leaves a launch pad at Cape Kennedy, moving vertically with an acceleration of 36.0 m/s2. If the speed of the exhausted gases is 4.50 3 103 m/s, at what rate is the rocket initially burning fuel?
(a) 3.05 3 103 kg/s
(b) 2.40 3 103 kg/s
(c) 7.50 3 102 kg/s
(d) 1.50 3 103 kg/s
(e) None of these

Answer 1

Answer:

(b) 2.40 x $10^{3}$ kg/s

Explanation:

Given that: Total mass of the rocket = 3.003 x $10^{5}$ kg

acceleration of the rocket = 36.0 m$s^{-2}$

speed of the exhausted gases = 4.503 x $10^{3}$ m/s

Rate at which rocket was initially burning fuel = $\frac{mass}{time}$

But,

time = $\frac{velocity}{acceleration}$

       = $\frac{4.503*10^{3} }{36.0}$

       = 125.0833 s

So that;

Rate at which rocket was initially burning fuel = $\frac{3.003*10^{5} }{125.0833}$

        = 2400.8001

        = 2.40 x $10^{3}$ kg/s

Therefore, the initial rate at which the rocket burn fuel is 2.40 x $10^{3}$ kg/s.