Question

distance distance = speed x time

1. how far can you get away from your little brother with the squirt gun filled with paint if you can travel at 3 m/s and you have 15s before he sees you?
2. how far can your little brother get if he can travel at 2.5 m/s and in 5 seconds you will discover that his squirt gun has run out of paint?
3. if you shout into the grand canyon, your voice travels at the speed of sound (340 m/s) to the bottom of the canyon an back, and you hear an echo. how deep is the grand canyon at a spot where you can hear your echo 5.2 seconds after you shout?

Explanation:

Step1: Use the formula \(d = v\times t\)

For problem 9: \(v = 3\ m/s\), \(t=15\ s\). So \(d = 3\times15\)

Step2: Calculate the product

\(3\times15=45\)

For problem 10: \(v = 2.5\ m/s\), \(t = 5\ s\). So \(d=2.5\times5\)

Step3: Calculate the product

\(2.5\times5 = 12.5\)

For problem 11: The sound travels to the bottom and back. Let the depth of the canyon be \(h\). The total distance traveled by sound is \(d = 2h\). \(v = 340\ m/s\), \(t = 5.2\ s\). Using \(d=v\times t\), we have \(2h=340\times5.2\)

Step4: Solve for \(h\)

First, calculate \(340\times5.2=1768\). Then \(h=\frac{1768}{2}=884\)

Answer:

1. \(45\ m\)
2. \(12.5\ m\)
3. \(884\ m\)