A landing craft of mass 12,000 kg prepares itself for a moon landing. When at a

Question

A landing craft of mass 12,000 kg prepares itself for a moon landing. When at a verticle distance of 160m above the surface of the moon its downward velocity is 15m/s-1. A retro-rocket is fired to give the spaceship an upward thrust to clow its speed to zero as it meets the surface.

Calculate the needed thrust to decelerate the crafts initial downward velocity to zero as it lands.

The value for gravity on the moon is g/6. where g = 9,81m/s2

Use a diagram to illustrate the above. A diagram is very important.

Thank you!

Will give excellent feedback if I receive a decent response...

Explanation / Answer

The force has to do work on the craft equal to the sum of the gravitational potential energy that it has 160 m up, and the kinetic energy it has moving at 15 m/s.

U = mgh = (12000 kg)(9.81/6 m/s2)(160 m) = 3.1392 * 106 J

K = (1/2)mv2 = (6000 kg)(15 m/s)2 = 1.350 * 106 J

for a total of 4.4892 * 106 J. Work is force times distance, so if you do the division you see that a force of 28057.5 N applied across 160 m does the job.

As for the diagram, can't do that for you but it's nothing ... a square representing the ship with one vector pointing up representing the upward force vector, and another one point down equal to mg.

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