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Chapter 12: Q65P (page 328)

(I) The wake of a speedboat is 12° in a lake where the speed of the water wave is 2.2 km/h. What is the speed of the boat?

Short Answer

Expert verified

The speed of the boat is \(10.58\;{\rm{km/h}}\).

Step by step solution

01

Understanding the relation to find the speed of the boat

In this problem, the angle made by the speedboat will be equivalent to the fraction of the speed of the water wave and speed of the boat.

02

Given Data

The angle is\(\theta = 12^\circ \).

The speed of the water wave is \(v = 2.2\;{\rm{km/h}}\).

03

Evaluating the speed of the boat

The relation to find speed is given by,

\(\sin \theta = \frac{v}{{{v_0}}}\)

Here, \({v_0}\) is the speed of the boat.

On plugging the values in the above relation.

\(\begin{aligned}{c}\sin 12^\circ &= \left( {\frac{{2.2\;{\rm{km/h}}}}{{{v_0}}}} \right)\\{v_0} &= 10.58\;{\rm{km/h}}\end{aligned}\)

Thus, \({v_0} = 10.58\;{\rm{km/h}}\) is the required speed.

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