Question

A baseball 4 feet off the ground is hit with an upward velocity of 52 feet per second.
The height of the baseball in feet after t seconds is given by the equation
h = – 1672 + 52t + 4. A fan catches the ball 16 feet off the ground when it is coming
down. When does the fan catch the ball?
The fan catches the ball
seconds after it is hit.
(Note: the ball is 16 feet high at one point when it is going up and again when it is
coming down.)
The solution is

Answer 1

Answer: The fan catch the ball after 3 seconds.

Step-by-step explanation:

Given,  A baseball 4 feet off the ground is hit with an upward velocity of 52 feet per second.

The height of the baseball in feet after t seconds is given by the equation

$h = - 16t2 + 52t + 4$

If a fan catches the ball 16 feet off the ground when it is coming  down.

then, at that time h= 16  feet

At h= 16

$16=-16t^2+52t+4\\\\\Rightarrow\ 16t^2-52t+12=0\\\\\Rightarrow\ 4t^2-13t+3=0$

$\Rightarrow\ 4t^2-t-12t+3=0\Rightarrow\ t(4t-1)-3(4t-1)=0\\\\\Rightarrow\ (4t-1)(t-3)=0\\\\\Rightarrow\ t=\dfrac{1}{4},\ t=3$

From the graph , it can be observe that when ball comes back , for height 16 feet the corresponding time t= 3 sec

So, the fan catch the ball after 3 seconds.