Applications Involving Quadratic Functions

Question

A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25°. The height of the ball can be modeled by h(t) = -16t² + 30.4t + 5 where h(t) is the height (in ft) and t is the time in seconds after release.

a. Determine the time at which the ball will be at its maximum height.
b. Determine the maximum height of the ball.
c. Determine the amount of time required for the ball to reach the receiver’s hands if the receiver catches the ball at a point 3 ft off the ground.

Answer 1

a)

 

Use the equation

 

t = -b / (2a)

 

where:

a = -16

b = 30.4

 

Plug these values into the equation.

 

 

b)

 

Evaluate h(t) at the time of maximum height.  The time of maximum height is the value found in previous part.

 

 

c)

 

Set  h(t) equal to 3 and solve for t.

 

3 = -16t² + 30.4t + 5

 

0 = -16t² + 30.4t + 2

 

 

Solve this quadratic equation for t.  I suggest you use the quadratic formula to solve for.  Choose the positive t value.