Equations , Problem 4

Question

Problem 4:

A fan sitting behind the dug-out catches a foul ball. He returns the ball to the umpire. The height of the ball h(t) above the ground (measured in meters) as a function of time (measured in seconds and represented by the variable t) from the instant of the release from the fan’s hand can be represented by the following equivalent forms:

Equation 1:

Equation 2:

Equation 3:

1. Which equation is the most useful for finding how many seconds it takes the ball to hit the ground? Why? How long is the ball in the air?

2. Which equation is the most useful for finding how many seconds it takes the ball to reach the maximum height? Justify your answer? How long does it take? What is the maximum height of the ball?

3. Which equation is the most useful for finding how high the ball was after one second? Why did you choose that one? What is the height at one second?

4. If you wanted to know the height of the bleacher that the fan was standing on, which equation would you use? Why? What is the height that the fan is standing (in meters) when he threw the ball?

5. If you were to make an equation to model the height of the ball that would be thrown from the ground level, what might it be? Explain how you determined that equation, and why you chose that form to use.

Answer 1

1) Which one is easiest to solve when set equal to ZER0???

I would choose the second one, which says 3.12 seconds

2) The max height occurs at the vertex which is exploited

by equation #3, as t=1.4 and the max height is 14.8

3) well, 1 to any power is 1, so the first equation says

the height h(1) = -5+14+5 = 14

4) at time t=0, the initial height is 5 per the first equation,

since zero to any power is zero

5) then the initial height is zero at time zero; that is h(0) = 0