Question: Edward stands on a bridge 73.5 feet above the ground holding an apple. He throws it with an initial downward velocity of -25 feet per second. How long will it take for the apple to reach the ground, if the vertical motion is given by the equation h = -16t2 + vt + s?
A ) 1.5 seconds B ) 3.06 seconds C ) 2 seconds D ) 2.5 seconds
Steps to derive
1h = -16t2 + vt + s [Original equation.]
2 0 = -16t2 + vt + s [h = 0 for ground level.]
3 0 = -16t2 - 25t + 73.5 [Replace v with -25 and s = 73.5.]
4t = [-(-25)±[(-25)²-4(-16)(73.5)]]2(-16) [Substitute the values of a = -16, b = -25 and c = 73.5 in the quadratic formula.]
5 = [25±(625+4704)]-32 [Evaluate the power and multiply.]
6 = 25±5329-32 [Add within the grouping symbols.]
7 = 25±73-32 [Find the square root.]
8t = -3.0625 or 1.5 [Simplify.]
9 The apple will reach the ground about 1.5 seconds after it was thrown.
