Question

A ball is kicked from a height of 3 feet above the ground. The height of the ball, h(t), is given by h(t) = -5t^2 + 14t + 3, where *t* is the time in second after the ball is kicked. How long will it take the ball to hit the ground after it is kicked?
A) 3.0 seconds

B) 3.4 seconds

C) 0.2 second

D) -0.2 second

Answer 1

check the picture below.

so the ball hits the ground when y = 0, namely h(t) = 0.

$\bf \stackrel{h(t)}{0}=-5t^2+14t+3\implies 5t^2-14t-3=0\implies (5t+1)(t-3)=0 \\\\[-0.35em] ~\dotfill\\\\ 5t+1=0\implies 5t=-1\implies t=-\cfrac{1}{5} \\\\[-0.35em] ~\dotfill\\\\ t-3=0\implies \boxed{t=3}$

we can't use the -1/5 because, the seconds after 0, can't be negative.