If a rock is thrown upward on the planet Mars with a velocity of 11 m/s, its hei

Question

If a rock is thrown upward on the planet Mars with a velocity of 11 m/s, its height in meters t seconds later is given by y = 11t ? 1.86t2. (Round your answers to two decimal places.)

If a rock is thrown upward on the planet Mars with a velocity of 11 m/s, its height in meters t seconds later is given by y = 11t ? 1.86t2. (Round your answers to two decimal places.) Find the average velocity over the given time intervals. please show how to do it for at least one set of numbers i am really lost on the set up for it. we have not used derivatives like power or chain rule yet. Estimate the instantaneous velocity when t = 1.

Explanation / Answer

y = 11t ? 1.86t^2
velocity = dy/dt = 11 - 2*1.86t
v = 11 - 3.72t

When t = 1: v = 11 - 3.72 = 7.28

When t = 2: v = 11 - 7.44 = 3.56
Average [1, 2] = (7.28 + 3.56 ) / 2 = 5.42m/s

When t = 1.5: v = 11 - 5.58 = 5.42
Average [1, 1.5] = (7.28 + 5.42 ) / 2 = 6.35m/s

When t = 1.1: v = 11 - 4.092 = 6.908
Average [1, 1.1] = (7.28 + 6.908) / 2 = 7.094m/s

When t = 1.01: v = 11 - 3.7572 = 7.2428
Average [1, 1.01] = (7.28 + 7.2428) / 2 = 7.2614m/s

When t = 1.001: v = 11 - 3.72372 = 7.27628
Average [1, 1.001] = (7.28 + 7.27628) / 2 = 7.27814m/s

(b) 7.28m/s

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