Question

Recall that the height of an object t seconds after it begins moving when gravity is the only force acting on the object is given by
h(t)=−16t2+v0t+h0,
where h(t) is given in feet, v0 is the initial velocity of the object in ft/sec, and h0

is the initial height of the object in feet.

If a ball is thrown directly upward from the top of a building with an initial velocity of 60
feet per second, and an initial height of 75 feet. What is the maximum height attained by the ball?
Your answer is feet.

Answer 1

Y = -16 t^2 + Vo t + Ho

Vo = 60 feet/s
Ho = 75 feet

y = - 16 t^2 + 60 t + 75

The maximum heigth correspond to the vertex of the parabola

You can find it by finding the roots using the quadratic equation (which I let to you) or by finding the highest value using derivatives (which I do next):

y' = -32 t + 60 = 0 => t = 60/32 = 1.875

y = -16 (1.875)^2 + 60 (1.875) + 75 = 131.25 feet.

Answer: 131.25 feet.