A 12,000-kg lunar landing craft is about to touch down on the surface of the moon, where the acceleration due to gravity is 1.6 m/s2. At an altitude of 158 m the craft's downward velocity is 16.9 m/s. To slow down the craft, a retrorocket is firing to provide an upward thrust. Assuming the descent is vertical, find the magnitude of the thrust needed to reduce the velocity to zero at the instant when the craft touches the lunar surface. In newtons.

Question

Physics

David Mullen

14 January, 07:10

A 12,000-kg lunar landing craft is about to touch down on the surface of the moon, where the acceleration due to gravity is 1.6 m/s2. At an altitude of 158 m the craft's downward velocity is 16.9 m/s. To slow down the craft, a retrorocket is firing to provide an upward thrust. Assuming the descent is vertical, find the magnitude of the thrust needed to reduce the velocity to zero at the instant when the craft touches the lunar surface. In newtons.

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Micah Moran · Answer 1

F = 8354.05 N

Explanation:

m = 12000 Kg

g = 1.6 m/s²

y = 158 m

vi = 16.9 m/s

vf = 0 m/s

F = ?

We can apply the following equation

F - W = - m*a ⇒ F = W - m*a ⇒ F = m*g - m*a = m * (g-a) (I)

As a is an unknown magnitude, we can use the formula

vf² = vi² - 2*a*y ⇒ 0 = vi² - 2*a*y ⇒ a = (vi²) / (2*y)

then

a = (16.9 m/s) ² / (2*158 m) = 0.9038 m/s²

Now we use the equation I

F = (12000 Kg) * (1.6 m/s² - 0.9038 m/s²) = 8354.05 N