Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1 point 5 ft/s. When Graham’s arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?
Answer
A
h is equal to 18 plus 1 point 5 t minus 16 t squared h is equal to 5 plus 24 t minus 16 t squared
B
h is equal to 18 plus 1 point 5 t h is equal to 5 plus 24 t
C
h is equal to 18 plus 1 point 5 t h is equal to 5 plus 24 t minus 16 t squared
D
h is equal to 18 plus 1 point 5 t h is equal to 5 plus 24 t plus 16 t squared
Explanation
Let t be the time in seconds after Hunter throws the ball, and h be height in feet. Graham starts at 18 ft and rises at a constant 1.5 ft/s, so his height is h = 18 + 1.5t. The ball starts at 5 ft with upward velocity 24 ft/s and is affected by gravity, giving h = 5 + 24t − 16t². These are the equations in choice D.
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