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 gia b. After the first impact, this contraption bounced back up to the height from which it was dropped. One might picture a stunned 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?

Explanation / Answer

Let the height be h and time it takes to fall to the surface is t.

h = 0.5 at^2

h = 0.5*3.74*t^2

now, [0.5*3.74*(t-1.04)^2] - [0.5*3.74*(t-1.04-0.68)^2] = 5

solving equation, t = 3.346 s

height h = 0.5*3.74*3.346^2

= 20.94 m answer

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