SOLUTION: Charlie Brown punts a football, which leaves his foot at a height of 3 ft above the ground and with an initial upward velocity of 70 ft/sec. The vertical velocity of the football t
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Question 1116036: Charlie Brown punts a football, which leaves his foot at a height of 3 ft above the ground and with an initial upward velocity of 70 ft/sec. The vertical velocity of the football t seconds after it is punted is given by v(t)=-32t+70, where v is in feet per second.(Note that velocity is the derivative of height.)
After how many seconds does the ball reach its highest point, and how high is the ball at this point? Answer by ikleyn(52781) (Show Source):
The ball will complete its movement vertically up when its vertical velocity becomes equal to zero:
v(t) = -32*t + 70 = 0.
It implies t = = = seconds = 2.1875 seconds.
To get the maximum height, you need EITHER integrate the formula for velocity over time, OR know and use the classic formula for it
h(t) = -16*t^2 + 70t + 3
where 3 = 3 ft = initial height of the ball.
This formula goes from Physics or from Algebra course.
Substitute t = 2.1875 into the formula and get your answer.
