A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by th

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 t seconds after it is hit is given by the quadratic function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 9.8 t plus 1h(t)=−4.9t2+9.8t+1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?

Answer 1

h(t) = -4.9t² + 9.8t + 1

 

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

 

t = -9.8/[2(-4.9)] s = 1 s

 

h_max = h(1) = [-4.9(1²) + 9.8(1) + 1] m = 5.9 m

Answer 2

The length of time and the maximum height can be found by finding the vertex of the parabola.

h(t) = -4.9t² + 9.8t + 1

x = -b/2a

t = -9.8/-9.8 

t = 1 second

h(1) = -4.9(1)² + 9.8(1) + 1

h(1) = -4.9 + 9.8 + 1

h(1) = 5.9 meters    V(1,5.9)