Question

Pekka tosses a ball out of a window that is 40 feet in the air. Its initial velocity is 15
feet per second. The path of the ball is represented by
h = -16t2 + 15t + 40
How long does it take for the ball to hit the ground (in seconds) rounded to the
nearest hundredth?

Answer 1

Answer:

2.12 seconds

Step-by-step explanation:

Given

$h(t) = -16t^2 + 15t + 40$

Required

Determine how long the ball hits the ground

When the ball hits the ground means that $h(t) = 0$

So, we have that:

$h(t) = -16t^2 + 15t + 40$ becomes

$0 = -16t^2 + 15t + 40$

Reorder

$-16t^2 + 15t + 40 = 0$

Multiply through by -1

$16t^2 - 15t - 40 = 0$

Solve using quadratic:

$t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

Where

$a = 16$ $b = -15$ $c = -40$

So, we have:

$t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$ becomes

$t = \frac{-(-15)\±\sqrt{(-15)^2 - 4*16*-40}}{2*16}$

$t = \frac{15\±\sqrt{(-15)^2 - 4*16*-40}}{2*16}$

$t = \frac{15\±\sqrt{225 +2560}}{32}$

$t = \frac{15\±\sqrt{2785}}{32}$

$t = \frac{15\±52.77}{32}$

Split:

$t = \frac{15+52.77}{32}$ or $t = \frac{15-52.77}{32}$

$t = \frac{67.77}{32}$ or $t = \frac{-37.77}{32}$

$t = 2.12$ or $t = -1.18$

But time can't be negative

So:

$t = 2.12$

Hence, time to hit the ground is 2.12 seconds