Question

a boat attempts to travel straight across to the other side of a river. the boat can go 21 m/s and the river travels at 12 m/s. at what angle (to the nearest degree) does the boat need aim upstream to dock exactly on the other side of the river?

Explanation:

Step1: Use trigonometric relationship

Let the angle the boat aims upstream be \(\theta\). The velocity of the river \(v_r = 12\space m/s\) and the velocity of the boat \(v_b=21\space m/s\). We know that \(\sin\theta=\frac{v_r}{v_b}\) (using the right - triangle formed by the boat's velocity relative to water, the river's velocity, and the resultant velocity).

Step2: Calculate the angle

Substitute \(v_r = 12\) and \(v_b = 21\) into \(\sin\theta=\frac{v_r}{v_b}\). So \(\sin\theta=\frac{12}{21}\approx0.5714\). Then \(\theta=\sin^{- 1}(0.5714)\).

Using a calculator, \(\theta\approx35^{\circ}\)

Answer:

\(35^{\circ}\)