Question

a swimmer swims perpendicular to the bank of a 30.0 m wide river at a velocity of 2 m/s. suppose the river has a current of 3m/s w. (a) how long does it take the swimmer to reach the other shore? (b) how far downstream does the swimmer land from his intended location?

Explanation:

Step1: Calculate time to cross river

The swimmer's velocity perpendicular to the bank \(v_y = 2\ m/s\), and the width of the river \(d = 30.0\ m\). Using the formula \(t=\frac{d}{v_y}\).

$$t=\frac{30.0}{2}=15\ s$$

Step2: Calculate distance downstream

The river current velocity \(v_x = 3\ m/s\), and the time \(t = 15\ s\). Using the formula \(x = v_x\times t\).

$$x=3\times15 = 45\ m$$

Answer:

(a) \(15\ s\)
(b) \(45\ m\)