Tower Escape is one of the most popular thrill rides at Mountain Adventure amusement park. It lifts riders to the top of a tower and drops them from a height of 200 feet. The riders fall to a height of 75 feet, at which point magnetic brakes slow them down.

Question

Which equation can you use to find how many seconds the riders fall before slowing down?
If an object falls from s feet above the ground, the object's height in feet, h, after t seconds can be modeled by the formula h=
–
16t2+s.
To the nearest tenth of a second, how long do the riders fall before slowing down?
seconds

Answer 1

To find the time \( t \) it takes for the riders to fall from a height of 200 feet to a height of 75 feet, we can use the given formula for the height of an object in free fall:

\[ h = -16t^2 + s \]

Here, \( s \) is the initial height from which the riders are falling, which in this case is 200 feet. We want to find the time \( t \) when the height \( h \) is 75 feet.

1. Substitute \( s = 200 \) and \( h = 75 \) into the formula:

\[ 75 = -16t^2 + 200 \]

2. Rearranging the equation:

\[ -16t^2 + 200 = 75 \]

Subtract 200 from both sides:

\[ -16t^2 = 75 - 200 \] \[ -16t^2 = -125 \]

3. Now, divide both sides by -16:

\[ t^2 = \frac{125}{16} \]

4. Take the square root of both sides to solve for \( t \):

\[ t = \sqrt{\frac{125}{16}} = \frac{\sqrt{125}}{4} = \frac{5\sqrt{5}}{4} \text{ seconds} \]

5. To approximate \( t \):

First, calculate \( \sqrt{5} \) (approximately 2.236):

\[ t \approx \frac{5 \times 2.236}{4} \approx \frac{11.18}{4} \approx 2.795 \]

Now, round this to the nearest tenth:

\[ t \approx 2.8 \text{ seconds} \]

So, the riders fall approximately 2.8 seconds before slowing down.