Page 77 - Calc for the Clueless

C. Find the velocity when the ball hits the ground.

A. v' = a = -20 (gravity is down). Take antiderivative—

y(0) = 50, sooooo the equation for the height is

B. Throw something lightish into the air straight up. You see that the object stops at its maximum height. This
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means v = -20t + 40 = 0. t = 2. Substituting into the equation for the height y, we get y = -10(2) + 40(2) + 50 =
90 feet, its maximum height.

C. The ground, as noted before, is y = 0. So

Rejecting t = -1 (negative time is before the object is thrown upward), we get t = 5. Substituting t = 5 into the
velocity equation, we get ...

where the minus sign indicates that the object is going down when it hits the ground.

Note

Since we live on the planet Earth, it would be a good idea to memorize the formulas for throwing an object
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upward: y = -16t + v 0t + y 0 in feet and y = -4.9t + v 0t + y 0 in meters.
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