About how long after it was thrown does it go into the hoop?

Question

A basketball is thrown with an initial upward velocity of 23 feet per second from a height of 7 feet above ground. The equation h=-16t^2+23t+7 models the height in feet 't' seconds after the basketball is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?

Answer 1

Lxsh,

 

h = -16t² + 23t + 7 (according to the model given).  We want to know what t is when h = 10.

 

10 = -16t² + 23t + 7

 

0 = -16t² + 23t - 3 (subtract 10 from both sides)

 

Factor the quadratic (use the quadratic formula or your calculator).

 

When you do, t = (.145sec, 1.292sec) - remember, there are two times when h = 10; on the way up and on the way down.

 

So, when it goes through the hoop, it's on its way down (hopefully ;-)

 

So, t = 1.292 sec.