Question

2. A small ball is tossed from a tall building. The function, h given by

h(t) = 100+ 30t - 16t² shows the ball's height, in feet, t seconds after it was
dropped.
Select all statements that are true about the situation.
a. The value t=8 does not belong in the domain of h.
b. The domain of function h can be all real numbers.
c. The ball has hit the ground in 4 seconds.
d. The ball has hit the ground in 2 seconds.
e. The ball was tossed from the building at 30 feet.

Answer 1

Explanation:

Set h=0 for ground height, then solve for t

-16t^2 -20t +240 = 0

divide by -4

4t^2 +5t - 60 = 0

use the quadratic formula

t= -5/8 + or - (1/8)square root of (25 +4(4)(60)). Ignore the negative square root

=-5/8 + (1/8)sqr(960+25)

= -5/8 + (1/8)sqr(985)

=-5/8 + (1/8)sqr(5(197))= slightly less than -5/8 +(10/8)(sqr10) = about -5/8 +32/8 = 27/8 = 3.3 seconds

the ball's initial velocity is negative, meaning the ball was thrown downward. Then add the effect of gravity, and it should hit the ground in a short time, even when thrown from an initial height of 240 feet.

plug t=2 into the original equation for height. You should get slightly above ground, near zero

-16(2)^2 -20(2) +240 = -64 -40+240 = 136

try t=3

-16(9) -20(3) +240 = -144 -60 +240 = 36

try t=4

-16(16) -20(4) +240 =-256 -80 +240 =-96

the time to hit ground should be between t=3 and 4, but closer to t=3, maybe about 3 1/3 seconds