Question

A child in danger of drowning in a river is being carried down-stream by a current that flows uniformly with a speed of 2.20 m/s . The child is 500 m from the shore and 1100 m upstream of the boat dock from which the rescue team sets out.
If their boat speed is 7.30 m/s with respect to the water, at what angle from the shore must the boat travel in order to reach the child?

Answer 1

Answer:

The angle is 65.6°.

Explanation:

Given that,

Speed = 2.20 m/s

Distance from the shore= 500 m

Distance from the bottom= 1100 m

Speed of boat = 7.30 m/s

According to figure,

We need to calculate the angle with shore

Using formula of angle

$\tan\theta=\dfrac{y}{x}$

Put the value into the formula

$\tan\theta=\dfrac{500}{1100}$

$\theta=\tan^{-1}(\dfrac{500}{1100})$

$\theta=24.4^{\circ}$

We need to calculate the angle

$\alpha=90-\theta$

Put the value into the formula

$\alpha=90-24.4$

$\alpha=65.6^{\circ}$

Hence, The angle is 65.6°.