Question

A boat moving at 7.8 km/hr relative to the water is crossing a river 3.5 km wide in which the current is flowing at 2.8 km/hr. At what angle upstream should the boat head to reach a point on the other shore directly opposite the starting point?

Answer 1

Answer:$\theta =21.03^{\circ}$

Explanation:

Given

velocity of boat with respect to river $=7.8 km/hr$

velocity of river is $2.8 km/hr$

River is 3.5 km wide

Suppose boat leaves at an angle of $\theta$  with vertical such that it reaches exactly opposite end of initial Point

Therefore

$7.8\sin \theta$component will balance the river Flowso that sin component helps to cross the river

$7.8\sin \theta =2.8$

$\sin \theta =0.3589$

$\theta =sin^{-1}(0.3589)$

$\theta =21.03^{\circ}$