Question

A ball is thrown straight upward from a bridge and then falls all the way to the ground (past the

Answer 1

Answer:

t = 4.6 seconds

Step-by-step explanation:

The ball's height above the ground t seconds later is given by the  function is given by :

$h(t)=-16t^2+48t+120$

We need to find time when the ball be 20 feet above the ground. It means h(t) = 20.

So,

$-16t^2+48t+120=20\\\\-16t^2+48t+100=0$

The above is a quadratic equation, the solution of this quadratic equation is given by :

$t=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\t=\dfrac{-b+ \sqrt{b^2-4ac} }{2a},\dfrac{-b- \sqrt{b^2-4ac} }{2a}\\\\t=\dfrac{-48+ \sqrt{(48)^2-4\times (-16)(120)} }{2\times (-16)} \dfrac{-48-\sqrt{(48)^2-4\times (-16)(120)} }{2\times (-16)}\\\\t=-1.62\ s, 4.6\ s$

So, at t = 4.6 seconds, the ball will be 20 feet above the ground.