Chapter 6.7, Problem 35PPS

To determine

To Find:

If Isabel was 65 meters high when she dropped the keys, how many meters above the ground will the keys be after 2 seconds?

Answer to Problem 35PPS

1 meter.

Explanation of Solution

Given Information:

Isabel accidentally dropped her keys from the top of a Ferris wheel. The formula $t=\frac{1}{4}\sqrt{d-h}$  describes the time  t in seconds at which the keys are h meters above the ground and Isabel is d meters above the ground.

Given that Isabel was 65 meters above the ground and time is 2 seconds.

Concept Used :

Solve Radical equations:

• Isolate the radical on one side of the equation.
• Raise each side of the equation to a power equal to the index of the radical to eliminate the radical .
• Solve the resulting polynomial equation.Check your results.
• When solving radical equations, the result may be a number that does not satisfy the original equation . Such a number is called an extraneous solution.

Calculation:

• Given

  $t=\frac{1}{4}\sqrt{d-h}\text{ and }d=65;t=2$

$\begin{array}{l}\text{Substitute t=2 and d=65 in the equation }\\ t=\frac{1}{4}\sqrt{d-h}\\ \Rightarrow 2=\frac{1}{4}\sqrt{65-h}\\ \Rightarrow \text{8=}\sqrt{65-h}\mathrm{.....................}[\text{Multiply 4 each side]}\\ \Rightarrow {\left(\sqrt{65-h}\right)}^2=8^2\mathrm{............}[\text{Square both sides]}\\ \Rightarrow \text{6}5-h=64\\ \Rightarrow -h=64-\mathrm{65...............}[\text{Subtract 65 from each side]}\\ \Rightarrow h=\mathrm{1...........................}[\text{Multiply -1 each side]}\\ \text{Hence, the keys will be 1 meter above the ground after 2 seconds}\text{.}\end{array}$