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 the time to cross the river (for part a)

The motion of the swimmer perpendicular to the bank is independent of the river - current. The width of the river \(d = 30.0\space m\) and the velocity of the swimmer perpendicular to the bank \(v_y=2\space m/s\). Using the formula \(t=\frac{d}{v_y}\).

$$t=\frac{30.0\space m}{2\space m/s}$$

Step2: Calculate the downstream distance (for part b)

The time taken to cross the river \(t = 15\space s\) (from part a). The velocity of the river - current \(v_x = 3\space m/s\). Using the formula \(x=v_x\times t\).

$$x=3\space m/s\times15\space s$$

Answer:

a. \(t = 15\space s\)
b. \(x = 45\space m\)