5. The Mars Exploration Rovers, Spirit and Opportunity, were dropped embedded in

Question

5. The Mars Exploration Rovers, Spirit and Opportunity, were dropped embedded in a system of airbags that looed like a giant ball. After the first impact, this contraption bounced back up to the height from which it was dropped but astute observer of this scene on the solitary Martian surface, timing the giant ball's fall across two marks, separated by a vertical distance of 5m in 0.68s. The observer also timed the total amount of time the ball spends below the lower of the two marks to 1.04s If the surface gravitational acceleration on Mars is 3.74 m/s, and assuming that no speed is lost upon impact, what is the height from which the ball was dropped? . One might picture a stunned

Explanation / Answer

Use h = ut + (1/2)gt2

5 = u(0.68) + (1/2)(3.74)(0.68)2

u = 6.081 m/s

this is the velocity at the first mark

now, time from this point to the bottom is: t' = 0.68 + 1.04 = 1.72 s

so, using v = u + gt gives:

v = 6.081 + 9.8(1.72) = 22.937 m/s

now, the speed at the top from where the ball was dropped is zero. Using conservation of Energy,

(1/2)mv2 = mgH

H = 26.843 m

this is the height from which the ball was dropped.

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