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Question 138989: Frustrated with dealing with teh USEPA about the air pollution at his plant. Ricky took his cell phone and threw it off the top of his office building. the height h(t) of the falling cell phone at time (t) is described by the function:
h(t) = -16t^2 +64t +192
a) When will Ricky's phone be at height of 240 feet?
b) How many seconds will it take before Ricky's phone hits the ground?
Found 2 solutions by wagilo, solver91311:
Answer by wagilo(1)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! Both parts of this problem require you to determine the value of the variable when the value of the function is some given amount. The process is to replace  with the given value (240 feet for part a, 0 feet, i.e. the ground, for part b) and then solve the resulting quadratic equation.
In the first problem you are going to get 2 answers, both of them valid. That is because of a couple of facts that can be gleaned from the coefficient values in the function. First of all, the roof of the building plus the distance from Ricky's feet to the position of his hand when he released the phone is 192 feet from the ground. You know this because if you substitute 0 for time, i.e. the instant that he released the phone from his hand, the height of the phone was 192. Second, you know that the vertical component of the velocity with which he threw it was 64 feet per second UPWARD (because of the plus sign). Given the upward component the phone is going to go up until it reaches 240 feet, keep going to the maximum height it will reach, and then come back down again passing 240 feet on its way to the ground. Therefore, there are 2 answers to part a.
By the way, there is no way to really tell the angle from the horizontal that the phone's trajectory took, but it is safe to say that it was probably greater than 45 degrees. Even at 45 degrees, Ricky would have to have thrown a 91 mph fastball to get a 64 ft per second vertical component. Much less of an angle and it becomes beyond human capability to throw it that fast. For example, 30 degrees to the horiziontal would require that the velocity in the direction of the trajectory be about 188 miles per hour -- maybe Superman or the Incredible Hulk, but none of us mere mortals.
In the second part of the problem, you will also get 2 answers (you ALWAYS get two answers when you solve a quadratic), but one of them will be invalid because it will be negative, i.e. some number of seconds BEFORE he threw the phone. Just exclude that answer.
HINT: The quadratic equations in BOTH parts of this problem are factorable.
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