Frequently Asked Questions...
How high will the ball go given the 1st and 2nd derivative?
Use a(t) = -32 ft/sec² as the acceleration due to gravity. A ball is throne vertically upward from the ground with an initial velocity of 96 ft/sec. How high will the ball go?
Answer:
We have:
a(t) = -32 (given)
v(t) = ∫ a(t) dt = -32t + C
Since the initial velocity is 96 ft/s, v(0) = 96 and so C = 96. Thus:
v(t) = -32t + 96
Then:
s(t) = ∫ v(t) dt = -16t² + 96t + C
Since there is no initial movement, C = 0 and thus
s(v) = -16t² + 96t = -16t(t - 6).
The x-coordinate vertex of this occurs at (0 + 6)/2 = 3 (the average of the two zeroes). Then, the ball travels:
s(3) = -16(3)² + 96(3) = 144 feet.
Therefore, the ball goes 144 feet in the air.
I hope this helps!
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About the Author
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