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nignag [31]
3 years ago
8

A ball is thrown into the air at a velocity of 44 feet per second. Its height in feet, h after t seconds is represented by the e

quation h=12t^2+44t+16 after how many seconds will the ball hit the ground
Advanced Placement (AP)
1 answer:
Lady_Fox [76]3 years ago
6 0

Answer:

0.447 sec

Explanation:

velocity = distance/ time

distance 'h' is a function of time 't' given by

h = 12t^{2} + 44t + 16

⇒ differentiating equation

⇒ velocity = \frac{dh}{dt} = 24t + 44

⇒ acceleration = \frac{d^{2}h }{dt^{2} } = 24 \frac{ft}{sec^{2} }

deceleration due to gravity = -9.8 m/sec^{2} =  - 9.8 x 3.281 = - 32.154 ft/ sec^{2}

Net deceleration = 24 - 32.154 = - 8.15 ft/ sec^{2}

at maximum height v = 0

v^{2} = u^{2} + 2ah

⇒  0 = 44^{2} + 2 (-8.15)h

⇒ h = 118.72 ft⇒

118.72 = 12t^{2} + 44t + 16

⇒ 12t^{2} +44t - 102.72 = 0

⇒  t = -44 ± \sqrt{44^{2} - 4(12)(102.72) }     / (2 x 12)

t = 0.447 sec

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