What is the maximum height reached, and how long does it take for the arrow to reach the ground

Calculus
Tutor: None Selected Time limit: 1 Day

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

Oct 6th, 2015

Thank you for the opportunity to help you with your question!

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.

h'(t) = -36t + 160

0 = -36t + 160

36t = 160

t = 40/9

h(40/9) = -16(40/9)^2 + 160 * 40/9 + 8 = 403.06 ft

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

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 6th, 2015

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