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Jake tosses a coin up in the air and lets it fall on the ground. The equation that

models the height (in feet) and time (in seconds) of the parabola is

h(t) = -16t2 + 24 + 6. Approximate the time at which the coin hits the

ground.

User Leopik
by
8.3k points

1 Answer

3 votes

Answer:


t = 1.71825

Explanation:

Given


h(t) = -16t^2 + 24t + 6

Required

When will the coin hit the ground

When the coin hits the ground,
h(t) = 0

The expression
h(t) = -16t^2 + 24t + 6 becomes


0 = -16t^2 + 24t + 6

Multiply through by -1


16t^2 - 24t - 6 = 0

Solve using quadratic formula


t = (-b\±√(b^2 - 4ac))/(2a)

Where


a = 16


b = -24


c = -6


t = (-b\±√(b^2 - 4ac))/(2a)


t = (-(-24)\±√((-24)^2 - 4 *16 * -6))/(2 * 16)


t = (24\±√(576 +384))/(32)


t = (24\±√(960))/(32)


t = (24\±30.984)/(32)

Split


t = (24+30.984)/(32) or
t = (24-30.984)/(32)


t = (54.984)/(32) or
t = (-6.984)/(32)


t = 1.71825 or
t = -0.21825

But time can't be negative;

So:

Time to hit the ground is 1.71825 seconds

User SnoopFrog
by
8.1k points
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