Question

question 5 of 10
a boat sails along the shore. to an observer, the boat appears to move at a speed of 22 m/s, and a man on the boat walking forward appears to have a speed of 23.1 m/s. how long does it take the man to move 3 m relative to the boat?
a. 0.14 s
b. 1.3 s
c. 2.7 s
d. 0.13 s

Explanation:

Step1: Identify relative - speed

The relative speed of the man with respect to the boat is found by considering the speeds given. The speed of the boat is $v_{boat}=22\ m/s$ and the speed of the man with respect to the observer is $v_{man - observer}=23.1\ m/s$. The relative speed of the man with respect to the boat $v = v_{man - observer}-v_{boat}=23.1 - 22=1.1\ m/s$.

Step2: Use the speed - distance formula

The formula for speed is $v=\frac{d}{t}$, where $v$ is speed, $d$ is distance, and $t$ is time. We want to find the time $t$ when $d = 3\ m$ and $v = 1.1\ m/s$. Rearranging the formula for $t$, we get $t=\frac{d}{v}$.
Substitute $d = 3\ m$ and $v = 1.1\ m/s$ into the formula: $t=\frac{3}{1.1}\approx2.7\ s$.

Answer:

C. 2.7 s