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Question

The height h, in feet, of a golf ball t seconds after it has been hit is given by the equation h = −16t2 + 62t. How many seconds after the ball is hit will the height of the ball be 42 feet? Round answers to nearest hundredth.

Answer 1

h = 42

 

42 = -16t² + 62t

 

Move all terms to the left side to make the right side of equation zero.

 

16t² - 62t + 42 = 0

 

We have a quadratic equation.

 

 

Factor out the 2.

 

2(8t² - 31t + 21) = 0

 

 

Set  8t² - 31t + 21 equal to zero.

 

8t² - 31t + 21 = 0

 

 

Use the quadratic formula to solve for t.

 

t = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 8

b = -31

c = 21

 

t = (31 ± √(961 - 4(168)) / 16

t = (31 ± √(289)) / 16

t = (31 ± 17) / 16

t = (31 + 17) / 16           and          t = (31 - 17) / 16    

 

t = 48 / 16                      and          t = 14 / 16

 

t = 3                              and          t = 0.875

 

 

The ball will reach the height of 42 feet at 3 seconds.

Answer 2

-16t² + 62t = 42

 

-16t² + 62t - 42 = 0

 

8t² - 31t + 21 = 0

 

(8t - 7)(t - 3) = 0

 

t = 7/8 or t = 3

 

The height of the golf ball is 42 ft after 7/8 sec and after 3 sec.