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A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s⁻¹. To give an initial upward acceleration of 20 m/s², the amount of gas ejected per second to supply the needed thrust will be (g = 10 ms⁻²)

1. 127.5 kg s⁻¹
2. 187.5 kg s⁻¹
3. 185.5 kg s⁻¹
4. 137.5 kg s⁻¹

Correct answer: 187.5 kg s⁻¹

Solution

The thrust required is equal to the net force acting on the rocket. The net force is given by F = m(a + g), where m = 5000 kg, a = 20 m/s², and g = 10 m/s². Substituting, F = 5000 × (20 + 10) = 150,000 N. The thrust is also given by F = ṁv, where ṁ is the mass of gas ejected per second and v = 800 m/s. Solving for ṁ, ṁ = F/v = 150,000/800 = 187.5 kg/s.

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