The coin hits the ground after 10 seconds
The height in feet of a coin above the ground after t seconds is given by the equation:
h(t) = -16t² + 64t + 960
When the coin hits the ground the height h(t) would be zero feet. Hence, to determine the time at which the coin hits the ground, we substitute h(t) = 0 and find t. Hence:
-16t² + 64t + 960 = 0
-t² + 4t + 60 = 0
-t² + 10t - 6t + 60 = 0
t² - 10t + 6t - 60 = 0
t(t - 10) + 6(t - 10) = 0
(t + 6)(t - 10) = 0
t = -6 or t = 10
since the time cannot be negative, hence, t = 10
Therefore the coin hits the ground at 10 seconds
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