During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = -16
t2 + 56t and h = -16t2 + 156t - 248, where t is the time that has passed since the first ball was hit. Explain how to find the height at which the balls meet. Then find the height to the nearest tenth.
Sample response: Use substitution to set the equations equal to each other. Solve the resulting linear equation for time, t = 2.48 s. Substitute 2.48 into an equation to find the height, h.
To determine when both balls have the same height, equate the two equations and solve for t. h = -16t^2 + 56t h = -16t^2 + 156t - 248 -16t^2 + 56t = -16t^2 + 156t - 248 You can eliminate the -16t^2 terms leading to 56t = 156t - 248 => 0 = 100t - 248 => 248 = 100t => 2.48 = t Substituting this t value into either equation will provide the height. h = 16(2.48)^2 + 56(2.48) Final response: h = 40.4736 I hope this assists you:)
