To study how high a ball bounces, students drop the ball from various heights. The function h (t) = - 16t2 + h0 gives the height (in feet) of the ball at time t measured in seconds since the ball was dropped from a height of h0. If the ball is dropped from a height of 10 feet, find the elapsed time until the ball hits the floor. Round to the nearest tenth.

Question

Mathematics

Kaliyah Dudley

15 September, 13:47

To study how high a ball bounces, students drop the ball from various heights. The function h (t) = - 16t2 + h0 gives the height (in feet) of the ball at time t measured in seconds since the ball was dropped from a height of h0. If the ball is dropped from a height of 10 feet, find the elapsed time until the ball hits the floor. Round to the nearest tenth.

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Answers (1)

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Jazlyn Skinner · Answer 1

sqrt (10/16)

Step-by-step explanation:

h0 is the height it was dropped from, and the question says we drop a ball from a height of 10, so we have h0 = 10.

So now we have - 16t^2 + 10 and we want to know when the height is 0, so when - 16t^2 + 10 = 0. So it's just algebra, and solving for t will give us the time.

-16t^2 + 10 = 0

-16t^2 = - 10

t^2 = 10/16

t = sqrt (10/16)

Solving algebraically makes the negative an answe too, but you can't have a negative time. Go ahead and plug in to double check though.