Question 84077 • Common Core Algebra I 2014 - MA3109 B-CR
An object is launched into the air. The projectile motion of the object can be modeled using the functionh(t) = –16t2 + 72t + 5, where t is the time in seconds since the launch and h(t) represents the height in feet of the object after t seconds. What is true about the projectile motion of this object? Check all that apply.The initial height is 5 feet.The initial velocity of the object is –72 feet/second.The object will hit the ground after approximately 4.57 seconds.After 3 seconds, the object is 173 feet high.At t = 0, h(t) = 0.
Answer
A
The initial height is 5 feet.
B
The initial velocity of the object is –72 feet/second.
C
The object will hit the ground after approximately 4.57 seconds.
D
After 3 seconds, the object is 173 feet high.
E
At t = 0, h(t) = 0.
Explanation
At launch, t = 0, so h(0) = 5; the initial height is 5 feet. The coefficient of t is 72, so the initial velocity is 72 feet per second, not −72. To find when the object hits the ground, set h(t) = 0; the positive solution to −16t² + 72t + 5 = 0 is about 4.57 seconds. At 3 seconds, h(3) = −16(9) + 72(3) + 5 = 77 feet, not 173, and h(0) is not 0.
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