Question

exercise 1: in a boat race, dan drove his motorboat over the 1000 - meter course from start to finish in 40 seconds. what was dan’s average speed during the race? exercise 2: it takes serina 0.25 hour to drive to school. her route is 16 km long. what is serina’s average speed on her drive to school? exercise 3: in a competition, an athlete threw a flying disk 139 meters through the air. while in flight, the disk traveled at an average speed of 13.0 m/s. how long did the disk remain in flight? exercise 4: if you shout into grand canyon, your voice travels at the speed of sound (340 m/s) to the bottom of the canyon and back, and you hear an echo. how deep is the grand canyon in a spot where you can hear your echo 5.2 seconds after you shout? exercise 5: sound travels much faster in water than air. it takes 4.2 seconds for the sound of an explosion to travel underwater to a diver 6,006 m away. what is the speed of sound in water?

Explanation:

Step1: Recall speed - distance - time formula

The formula for speed is $v=\frac{d}{t}$, where $v$ is speed, $d$ is distance, and $t$ is time.

Step2: Solve Exercise 1

Given $d = 1000$ m and $t = 40$ s. Using the formula $v=\frac{d}{t}$, we have $v=\frac{1000}{40}=25$ m/s.

Step3: Solve Exercise 2

Given $d = 16$ km and $t = 0.25$ h. First, convert km to m and h to s if needed. Since $1$ km=$1000$ m and $1$ h = 3600 s, but we can also calculate in km/h. Using $v=\frac{d}{t}$, $v=\frac{16}{0.25}=64$ km/h.

Step4: Solve Exercise 3

Given $d = 139$ m and $v = 13.0$ m/s. Rearranging the formula $v=\frac{d}{t}$ to $t=\frac{d}{v}$, we get $t=\frac{139}{13.0}\approx10.69$ s.

Step5: Solve Exercise 4

The sound travels to the bottom and back. Let the depth of the canyon be $h$. The total distance traveled by the sound is $d = 2h$. Given $v = 340$ m/s and $t = 5.2$ s. Using $d=v\times t$, we have $2h=340\times5.2$. Then $h=\frac{340\times5.2}{2}=884$ m.

Step6: Solve Exercise 5

Given $d = 6006$ m and $t = 4.2$ s. Using the formula $v=\frac{d}{t}$, we get $v=\frac{6006}{4.2}=1430$ m/s.

Answer:

Exercise 1: 25 m/s
Exercise 2: 64 km/h
Exercise 3: Approximately 10.69 s
Exercise 4: 884 m
Exercise 5: 1430 m/s