If an arrow is shot upward on Mars with a speed of 68 m/s, its height in meters t seconds later is given by y = 68t − 1.86t^2. Estimate the speed when t=1

Answer 1

PROBLEM

If an arrow is shot upward on Mars with a speed of 68 m/s, its height in meters t seconds later is given by y = 68t − 1.86t^2. Estimate the speed when t=1

SOLUTION

The arrow's speed, v(t) would be the derivative of the equation for the height, dy/dt. Therefore, when t = 1 take the derivative of y(t) = 68t - 1.86t² and plug 1 into the equation for dy/dt.

QUESTIONS

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Answer 2

To solve this, plug t=1 into the equation provided.

y=68(1)-1.86(1)²

y=68-1.86

y=66.14 m/s

Answer 3

From given equation initial speed 68m/s, and accelaration of gravity g = 3.72 m/s^2

From this v = 68 - 3.72t, t = 1s, v = 68 - 3.72*1 = 64.28 m/s^2