Question

The height h in feet of a ball thrown vertically upward from the top of a 288-foot tall building is given by h=288+48t-16t^2 where t is in seconds. How long will it take to he penny to strike the ground.

Answer 1

6 sec can take penny to strike the ground.

Solution:

Given data:

$H_0=288$ feet

$V_0=48$ feet

$h(t)=288+48t-16t^2$

Re-arrange the terms from greatest degree to smallest degree.

$h(t)=-16t^2+48t+288$

We can solve it by applying quadratic formula,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here a = –16, b = 48, c = 288

$t=\frac{-48\pm \sqrt{48^2-4(-16)(288)}}{2(-16)}$

$t=\frac{-48\pm \sqrt{2304+18432}}{-32}$

$t=\frac{-48\pm \sqrt{20736}}{-32}$

$t=\frac{-48\pm144}{-32}$

Now, write find two t's using plus and minus operation.

$t=\frac{-48+144}{-32},\ \ t=\frac{-48-144}{-32}$

$t=\frac{96}{-32},\ \ t=\frac{-192}{-32}$

t = –3 (or)   t = 6

We cannot write time is negative. so neglect t = –3.

Therefore t = 6.

Hence 6 sec can take penny to strike the ground.