If an archer shoots an arrow straight upward with an initial velocity of 160 ft/sec from a height of 8 ft, its height above the ground in feet at the time t in seconds is given by the function h(t)= -16t^2+160t+8
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To find the maximum height reached, you have to take the derivative of the equation and find when the derivative equals 0. This will give you the time at which the maximum height is reached. Plug that time back into the original height equation to get the maximum height.
To find the time at which it hits the ground, set the original height equation equal to 0 and solve by using the quadratic equation or any other method you know of. There will be both a negative time answer and a positive time answer. The positive time will be when it hits the ground.
0 = -16t^2 + 160t + 8
t = [-160 +- sqrt(160^2 - 4*8*(-16))]/(2*-16)
t = 5 + sqrt(51/2) = 10.05
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