Maximum height? h(t)=-4.9t^2+24.5t+1

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+24.5t+1. How long does it take for the baseball to reach its maximum height?(in seconds) What is the maximum height obtained by the baseball?

Answer 1

Alexis,

 

Maximum height is reached at time t when the derivative of equation is zero

 

h(t) = -4.9t^2 + 24.5t + 1

 

d(h)/dt = -4.9*2*t + 24.5

 

Max height is when d(h)/dt = 0

 

so -9.8*t + 24.5 = 0

 

t = 24.5/9.8 = 2.5 seconds

 

The height is calculated by plugging t = 2.5 seconds in the height equation

 

Height at 2.5 seconds = -4.9*2.5^2 + 24.5*2.5 + 1

 

Which you can solve easily