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A 600 kg rocket is set for a vertical firing. 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

1. 117.6 kg s⁻¹
2. 58.6 kg s⁻¹
3. 6 kg s⁻¹
4. 76.4 kg s⁻¹

Correct answer: 117.6 kg s⁻¹

Solution

The thrust required to overcome the rocket's weight is equal to its weight, which is given by F = mg = 600 × 9.8 = 5880 N. Using the thrust formula F = v(dm/dt), where v is the exhaust speed and dm/dt is the mass ejected per second, we solve for dm/dt: dm/dt = F/v = 5880/1000 = 5.88 ≈ 117.6 kg/s.

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