The wake of a speedboat is $12 ^\circ$ in a lake where the speed of the water wave is 2.2 km/h. What is the speed of the boat?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The angle of the shock wave is calculated by taking the sine of it and that equals the speed of the wave when in the medium which is, you know, usually sound when we're talking about jet planes, divided by the speed of the object that's moving such as a plane. But we can also apply this to other types of waves such as a water wave. And so we have sine of the angle of this, between the velocity of the object and the shock wave is going to equal the speed of the water wave divided by the speed of the boat. So, we can multiply both sides by v object or boat in this case divided by sine θ and then on the left side we end up with speed of the boat equals speed of the water wave divided by sine θ. So, that's 2.2 kilometers per hour divided by sine 12. And that means the boat must be moving at about 11 kilometers per hour.