Please help with this math problem. -4.9t2 isn’t squared.

Question

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters is t seconds after the hit is given by the quadratic function h(t) = −4.9t2 + 34.3t + 1.

How could we calculate how long it takes the baseball to reach its maximum height? How could we calculate the maximum height obtained by the baseball? Find the maximum height of the baseball. Present all work where you found the maximum height of the baseball.

Answer 1

h(t) = -4.9t² + 34.3t + 1

 

The h vs. t curve is a concave-down parabola. Maximum h is at the vertex of this parabola, which is at 

 

t = -34.3[2(-4.9)] s = 3.5s

 

h_max = h(3.5) = [-4.9(3.5²) + 34.3(3.5) + 1] m = 61.025 m