Question

Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 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?
StartLayout Enlarged Left-Brace 1st Row h = 18 + 1.5 t 2nd Row h = 5 + 24 t minus 16 t squared EndLayout
StartLayout Enlarged Left-Brace 1st Row h = 18 + 1.5 t 2nd Row h = 5 + 24 t + 16 t squared EndLayout
StartLayout Enlarged Left-Brace 1st Row h = 18 + 1.5 t 2nd Row h = 5 + 24 t EndLayout
StartLayout Enlarged Left-Brace 1st Row h = 18 + 1.5 t minus 16 t squared 2nd Row h = 5 + 24 t + 16 t squared EndLayout

Answer 1

The first system:

h = 18 + 1.5t
h = 5 + 24t − 16t^2

Reason: Graham's height starts at 18 ft and increases at 1.5 ft/s. The ball starts 5 ft high with initial speed 24 ft/s and is affected by gravity, giving the −16t^2 term (half of 32 ft/s^2).