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

Step-by-step 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* cos37\hat{j}`

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

`|v_b|=√(0.413^2+5.98^2)`

`|v_b|=5.99 m/s`

Direction

`tan\theta =(5.98)/(0.413)=14.479`

`\theta =86.049^(\circ)` north of west