Question

H=-16t^2+122t+5 where h is height in feet and t is time in seconds. How long will it take the baseball to hit the ground? h=-16t^2+162t+0.2 where h is height in feet and t is time in seconds. How long will it take the golf ball to hit the ground?

Answer 1

Answer:

$t= 7.67$

$t= 10.13s$

Step-by-step explanation:

Solving (a):

$H=-16t^2+122t+5$

Required: Time to hit the ground

This means that H = 0

So, we have:

$0=-16t^2+122t+5$

Rewrite as:

$16t^2-122t-5=0$

Solve for t using:

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

$t= \frac{122 \± \sqrt{(-122)^2 - 4*16*-5}}{2*16}$

$t= \frac{122 \± \sqrt{15204}}{2*16}$

$t= \frac{122 \± 123.3}{32}$

Split:

$t= \frac{122 + 123.3}{32}$ or $t= \frac{122 - 123.3}{32}$

$t= \frac{245.3}{32}$ or $t= \frac{-1.3}{32}$

$t= 7.67$ or $t= -0.0406$

Time can not be negative. so: $t= 7.67$

Solving (b):

$h=-16t^2+162t+0.2$

Required: Time to hit the ground

This means that h = 0

$0=-16t^2+162t+0.2$

Rewrite as:

$16t^2-162t-0.2= 0$

Solve for t using:

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

$t= \frac{162 \± \sqrt{(-162)^2 - 4*16*-0.2}}{2*16}$

$t= \frac{162 \± \sqrt{26256.8}}{32}$

$t= \frac{162 \± 162.04}{32}$

$t= \frac{162 + 162.04}{32}$ or $t= \frac{162 - 162.04}{32}$

$t= \frac{324.04}{32}$ or $t= \frac{-0.04}{32}$

Time can not be negative. So:

$t= \frac{324.04}{32}$

$t= 10.13s$