Question

The water in a river moves south at 10 mi/hr. A motorboat travels due east at a speed of 20 mi/hr relative to the shore. Determine the speed and direction of the boat relative to the moving water.

Answer 1

Answer:22.36 mi/hr

Step-by-step explanation:

Given

water in a river moves south at $(V_w)10 mi/hr$

motorboat travels due to east at a speed of $(V_b)20 mi/hr$

Velocity of boat relative to the moving water $V_{bw}$

$V_{bw}=V_b-V_w$

$V_{bw}=20i-(-10j)=20i+10j$

Magnitude of $V_{bw}=\sqrt{20^2+10^2}=\sqrt{500}$

$V_{bw}=10\sqrt{5} \approx 22.36 mi/hr$

$tan\theta =\frac{10}{20}$

$\theta =26.56^{\circ}$ with the x axis.