Question

A 260-m-wide river flows due east at a uniform speed of 4.1m's A boat with a speed of 7 5ms relative to the water leaves the south bank pointed in a direction 37 west of north. What is the (al magnitiale and tb) direction ot the bat's velocity relative to the ground?

Answer 1

Answer:5.99 m/s

Explanation:

Given

Speed of river $(v_r)$=4.1 m/s

Width of river =260 m

Speed of boat$(v_{br})$=7.5 m/s

launch angle$=37^{\circ}$

$v_{br}=7.5(cos37\hat{j}-sin37\hat{i})$

$v_r=4.1\hat{i}$

Velocity of boat with respect to ground

$v_b=v_{br}+v_r$

$v_b=7.5(cos37\hat{j}-sin37\hat{i})+4.1\hat{i}$

$v_b=(-7.5sin37+4.1)\hat{i}+7.5\times cos37\hat{j}$

$v_b=-0.413\hat{i}+5.98\hat{j}$

$|v_b|=\sqrt{0.413^2+5.98^2}$

$|v_b|=5.99 m/s$

Direction

$tan\theta =\frac{5.98}{0.413}=14.479$

$\theta =86.049^{\circ}$ north of west