Upwards velocity using quadratic equations

Question

A basketball player shoots at the basket from a starting
height of 6 feet and an upwards velocity of 20 feet per second. Determine how long it
takes for the shot to drop through the basket, which is mounted at a height of 10 feet.

Answer 1

The height h as a function of time t is

 

h(t) = -16t² + 20t + 6,

 

with t in seconds, h in ft.

 

To find when the ball reaches 10 ft, set h = 10 and solve for t.

 

10 = -16t² + 20t + 6

 

-16t² + 20t - 4 = 0

 

Solve the quadratic equation for t and get t = 0.25 sec and 1 sec.  Since both are positive, it takes the ball 0.25 sec to reach 10 ft on the way up, and 1 sec to reach 10 ft again on the way down.  Since you want the ball to fall through the basket at 10 ft, use the time it takes coming back down to 10 ft, so your final answer is 1 sec.

Answer 2

h(t) = -16t² + 20t + 6

 

Set h(t) = 10          because you want to know when the ball reaches the position of the hoop.

 

-16t² + 20t + 6 = 10

 

-16t² + 20t - 4 = 0

 

 

Solve for t.

 

-4(4t² - 5t + 1) = 0

 

4t² - 5t + 1 = 0

 

(4t - 1)(t - 1) = 0

 

t = 1/4      and        t = 1

 

 

Since the ball has to land in the hoop, we chose the later t value.

 

t = 1

 

 

It takes 1 second for the shot to drop through the basket.