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(t)=-4.9t^2+29.4t+1. How long does it take for the baseball to reach maximum height? What is the maximum height obtained by the baseball?

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the tundtion h) -4.9+294t+1. How long doos it take for the basoball o reach its maximum height? What is the maximum t takes second(s) for the basoball to reach its maximum height baseball in metors t seconds afor it is hit is given by the quadratic (Round to one decimal place as needed.) The maximum height obtained by the baseballis meters. (Round to three decimal places as needed.)

Answer 1

1)
h(t) = -4.9*t^2 + 29.4*t + 1
differentiate with t to get velocity,
h’(t) = d/dt(h(t))
= d/dt(-4.9*t^2 + 29.4*t + 1)
= -4.9*2*t + 29.4
= -9.8t + 29.4

At maximum height, velocity is 0
so,
-9.8t + 29.4 = 0
t = 3.0 s
Answer: 3.0 s

2)
Lets find the height at this time
h(t) = -4.9*t^2 + 29.4*t + 1
at t=3.0 s,
h(3.0) = -4.9*(3.0)^2 + 29.4*(3.0) + 1
= -44.1 + 88.2 + 1
= 45.1 m

Answer: 45.1 m