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.)

Question

Mathematics

Leyla Gallegos

7 March, 23:48

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.)

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Answers (1)

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Rayne Anthony · Answer 1

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.