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 find the time at which both balls are at the same height, set the equations equal to each other then solve for t. h = -16t^2 + 56t h = -16t^2 + 156t - 248 -16t^2 + 56t = -16t^2 + 156t - 248 You can cancel out the -16t^2's to get 56t = 156t - 248 => 0 = 100t - 248 => 248 = 100t => 2.48 = t Using this time value, plug into either equation to find the height. h = 16(2.48)^2 + 56(2.48) Final answer: h = 40.4736 Hope I helped :)
