Mid-Chapter Quiz
8. SOCCER A soccer ball is kicked from ground level with an initial upward velocity of 90 feet per second. The
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equation h = −16t + 90t gives the height h of the ball after t seconds.
a. What is the height of the ball after one second?
b. How many seconds will it take for the ball to reach its maximum height?
c. When is the height of the ball 0 feet? What do these points represent in this situation?
SOLUTION: a. To find the height of the ball after one second, substitute t = 1 into the equation and solve for h.
The height is 74 feet after 1 second.
b. To find the maximum, find the line of symmetry.
So, the ball will reach its maximum height at 2.8125 seconds.
c. To determine when the ball is at 0 feet, substitute h = 0 into the equation and solve for t.
So, the height of the ball will be 0 feet before it is kicked at t = 0 and when it returns to the ground after the kick at t
= 5.625.
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13. BASEBALL Juan hits a baseball. The equation h = −16t + 120t models the height h, in feet, of the ball after t
seconds. How long is the ball in the air?
SOLUTION: To determine how long the ball is in the air, find the time when h = 0.
The ball will be in the air 7.5 seconds.
15. PARTIES Della’s parents are throwing a Sweet 16 party for her. At 10:00, a ball will slide 25 feet down a pole and
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light up. A function that models the drop is h = −t + 5t + 25, where h is height in feet of the ball after t seconds.
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many- seconds
will
it take for the ball to reach the bottom of the pole?
Mid-Chapter Quiz
The ball will be in the air 7.5 seconds.
15. PARTIES Della’s parents are throwing a Sweet 16 party for her. At 10:00, a ball will slide 25 feet down a pole and
2
light up. A function that models the drop is h = −t + 5t + 25, where h is height in feet of the ball after t seconds.
How many seconds will it take for the ball to reach the bottom of the pole?
SOLUTION: To determine how long it will take the ball to reach the bottom of the pole, put the equation into your graphing
calculator and choose a suitable window. Press 2nd, CALC, zero, and then choose a left and right bound to find when the ball reaches the bottom of the pole.
From the graph we can see that the ball reaches the bottom of the pole after 8.09 seconds.
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