Word problem

Question

Roscoe hit a ball straight up at a speed of 110 ft/sec. His bat hit the ball at a height of 3 feet above the ground. After how many seconds did the ball hit the ground?

Answer 1

The height above the ground is represented by the function

 

h(t) = y_i + v_it + (1/2)gt²

 

where:

h(t) = height above ground

y_i = initial height

v_i = velocity

g = acceleration due to gravity = 32 ft/s²

t = time

 

 

h(t) = -16t² + 110t + 3

 

 

To find how many seconds the ball hits the ground, set h(t) = 0

 

 

0 = -16t² + 110t + 3

 

 

Use the qudradtrac formula:

 

t = (-b ± √(b² - 4ac)) / 2a

 

where:

a = -16

b = 110

c = 3

 

Plug in these value into he formula to solve for t.  You will have 2 solutions because of he plus/minus sign.  Pick the positive value of t.