MATH SOLVE

7 months ago

Q:
# A potato is launched into the air at a velocity of 60 feet per second off of a building that is 210 feet tall. This can be modeled by the formula h=-16t^(2)+60t+210, where h is the height (in feet) after t seconds. When will the potato hit the ground? (Round to the nearest second.)

Accepted Solution

A:

The equation models the height of a projectile in feet above ground (h=0) with g=-32 ft/s^2 at a height of 210 ft. with an initial velocity (upwards) of 60 ft/s.

The time it takes to reach the ground can be obtained by solving the equation h(t)=0.

h(t)=0 =>

-16t^2+60t+210=0

=>

16t^2-60t-210=0

Solve by completing the square:

t^2-(60/16)t-210/16=0

=>

(t-60/32)^2=(60/32)^2-210/16

Simplify

t-15/8= ± sqrt(1065)/8

=>

t=15/8 ± sqrt(1065)/8

=-2.20 s. or 5.95 seconds (to two decimals).

Answer: after 5.95 seconds, the potato will hit the ground, assuming no air resistance.

The time it takes to reach the ground can be obtained by solving the equation h(t)=0.

h(t)=0 =>

-16t^2+60t+210=0

=>

16t^2-60t-210=0

Solve by completing the square:

t^2-(60/16)t-210/16=0

=>

(t-60/32)^2=(60/32)^2-210/16

Simplify

t-15/8= ± sqrt(1065)/8

=>

t=15/8 ± sqrt(1065)/8

=-2.20 s. or 5.95 seconds (to two decimals).

Answer: after 5.95 seconds, the potato will hit the ground, assuming no air resistance.