Question

the speed of a boat in still water is 25 mph. the boat is traveling on a river with a current flowing south at 10 mph. at what angle upstream should the boat head to travel due west? 21.80° 23.58° 66.42° 68.20°

Explanation:

Step1: Analyze the velocity vectors

Let the speed of the boat in still water be \(v = 25\) mph and the speed of the current be \(u=10\) mph.
If the boat heads at an angle \(\theta\) upstream, the vertical component of the boat's velocity (in still - water) should cancel out the velocity of the current.
The vertical component of the boat's velocity (in still water) is \(v\sin\theta\), and the velocity of the current is \(u = 10\) mph.

Step2: Set up the equation

We know that \(v\sin\theta=u\). Substituting \(v = 25\) mph and \(u = 10\) mph, we get \(\sin\theta=\frac{u}{v}\).

Step3: Solve for \(\theta\)

Since \(\sin\theta=\frac{10}{25}=0.4\), then \(\theta=\sin^{- 1}(0.4)\).
Using a calculator, \(\theta\approx21.80^{\circ}\).

Answer:

A. \(21.80^{\circ}\)