Answer:
Step-by-step explanation:
A science class designed a ball launcher and tested it by shooting a tennis ball up and off the top of a 15-story building. They determined that the motion of the ball could be described by the function: h(t) = -16t2 + 144t + 160, where ‘t’ represents the time the ball is in the air in seconds and h(t) represents the height, in feet, of the ball above the ground at time t.
a) Graph the function h(t) = -16t2 + 144t + 160 (see below)
b) What is the height of the building?
The height of the building is also the height of the tennis ball before it is launched into the air. This occurs when t=0 so substitute 0 for t and you get:
H(0) = -16(0)2 + 144(0) + 160
The height of the building is 160 feet.
c) At what time did the ball hit the ground?
The ball hits the ground when the height is 0. Therefore, we are looking for a solution to: -16t2 + 144t + 160 = 0
Use the quadratic formula or put this into a calculator. The solution is t=10 and -1, but only 10 makes sense. Therefore, the ball hits the ground at 10 seconds.
d) At what time did the ball reach its maximum height?
You can put this into the calculator or you can realize that the maximum height is also
− the vertex. The x-value (‘t’ in this case) is 2
−144
which is (2)(−16) = 4.5.
Therefore, the ball reached its maximum height at 4.5 seconds.
e) What is the maximum height of the ball?
We calculated the time of the maximum height (4.5 seconds). Therefore, substitute 4.5 into the function to find the maximum height.
-16(4.5)2 + 144(4.5) + 160
The maximum height is 484 feet.
