Question

A ball is thrown from an initial height of 3 feet with an initial upward velocity of 34 ft/s. The ball's height h (in feet) after t seconds is given by the following.

h=3+34t-16t^2

Answer 1

What is the maximum height of the ball and when does it occur?

To find the maximum height of the ball, we need to find the vertex of the parabolic function h(t) = 3 + 34t - 16t^2, which represents the height of the ball as a function of time. The vertex has a t-coordinate of -b/2a, where a = -16 and b = 34.

t = -b/2a = -34/(2*(-16)) = 1.0625

To find the corresponding height, we substitute t = 1.0625 into the equation for h(t):

h(1.0625) = 3 + 34(1.0625) - 16(1.0625)^2 ≈ 43.015625

Therefore, the maximum height of the ball is approximately 43.015625 feet, and it occurs after 1.0625 seconds.