Question

Special air bags are used to protect scientific equipment when a rover lands on the surface of Mars. On Earth, the function approximates an object's downward speed in feet per second as the object hits the ground after bouncing x ft in height. The corresponding function for Mars is compressed vertically by a factor of about 2/3. Estimate to the nearest tenth how fast a rover will hit Mars' surface after a bounce of 15 ft in height.

Answer 1

The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

What is the approximation about?

From the question:

Mars: F(x) = 2/3$\sqrt{64x}$

Therefore, If x = 15

Then:

f (15) =  2/3 $\sqrt[8]{15}$

= 16/3$\sqrt{15}$

= 20.7ft/s

Hence, The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.

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