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

The angle is 65.6°.

Step-by-step 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=(y)/(x)`

Put the value into the formula

`\tan\theta=(500)/(1100)`

`\theta=\tan^(-1)((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°.