First slide

Second law

Question

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20m / s², the amount of gas ejected per second to supply the needed thrust will be (g = 10m/s²)

Moderate

A

727.5kg/s
B

187.5kg/s
C

185.5 kg / s
D

137.5kg/s

Solution

Given, mass of rocket m = 5000 k8, exhaust speed u =800 m / s, acceleration of rocket a =20m/s²and g =10m/s²
Upward force F =T -W
or Ma=T-Mg
$\begin{array}{l} ∴ T = M [a + g] = 5000 [20 + 10] \\ = 15 \times 10^{4} N \end{array}$
Also, $T = u \frac{dM}{dt} or \frac{dM}{dt} = \frac{T}{u}$
$∴ \frac{d M}{d t} = \frac{15 \times 10^{4}}{800} = 187 \cdot 5 kg / s$

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