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Directions: Grab paper, pencil, and a graphing calculator. Be sure to show your algebraic work.
FORMULAS: Throw/Launch: Feet: h = -16t2 + v0t + h0 Meters: h = -4.9t2 + v0t + h0
Drop: remove middle term, v0t.
(h = height; t = time in seconds; v0 = initial (starting) velocity; h0 = initial (starting) height)
1. |
A model rocket is launched vertically upward from ground level with an initial velocity of 39.2 meters per second. Its height, h, after t seconds, is modeled by the equation h = -4.9t2 + 39.2t. How long, in seconds, will it take for the rocket to hit its maximum height?
Round to nearest hundredth.
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2. |
Conner is practicing his golf swing at the driving range. The height of the golf ball propelled by his swing is modeled by the equation
h = -16t2 +36t. If the ball is 18 feet in the air, during it's downward fall, how many seconds have passed since Conner hit the golf ball?
(Assume the ball is at ground level to start.)
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3. |
A loosened rock falls from the top of a 50 foot cliff into the ocean below. How long will it take for the rock to hit the surface of the water?
(State answer to the nearest hundredth of a second.)
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4. |
During baseball batting practice, Nate is pitched a ball with an initial velocity of 38 feet per second from a height of 5 feet.
Nate hits the ball after the ball has been airborne for 2.4 seconds.
What was the height of the ball when it was hit by Nate's swing?
(Round to nearest hundredth of a foot)
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5. |
Fireworks are shot into the air with an initial velocity of 30 meters per second from 10 meters above the ground. After being launched, how long will it take, in seconds, the fireworks to reach a height of 32 meters above its launch pad?
(Round to nearest hundredth of a second)
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6. |
At the end of a graduation ceremony, it is customary for the graduates to throw their mortar boards (hats) up into the air. Stacie tosses her hat into the air and it leaves her hand at 5 feet above the ground with an initial velocity of 20 feet per second. Find the maximum height reached by her hat.
(Do not round.)
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7. |
A dog throws his bone (from his mouth at 2 feet above the ground) up into the air at an initial velocity of 9 feet per second. How long will it take for the bone to return to a height of 2 feet above the ground?
(Round to nearest hundredth of a second.)
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8. |
Two balls are kicked upward from ground level. The white ball has an initial velocity of 35 feet per second and the blue ball has an initial velocity of 25 feet per second.
Find the difference between the airborne times of each of the balls.
(Do not round.)
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