7. The English Channel is 35 km wide at its narrowest point, which is where most swimmers attempt to cross north to south from England to France. The current across this portion of the English Channel runs at about 2 km/h east to west. a. If a swimmer has a relative velocity to the shore of 3 km/h north to south, how long will it take her to cross the 35 km distance?
b. What must be her velocity relative to the water if she has a velocity of 3 km/h north to south relative to the shore?

a. 10 hours

b. Approximately 4.03 km/h to shore

Explanation:

The width of the English Channel at the narrowest point = 35 km

The speed of the current across the English Channel across the narrowest point = 2 km/h

a. The relative velocity of the swimmer north to south = 3 km/h

Therefore, the the time it would take the swimmer to swim north to south will be given as follows;

Time = Distance/Velocity = 35 km/(3.5 km/h)  =10 hours

The time it would take = 10 hours

It would take 10 hours for her to cross the 35 km distance

b. Given that she has a relative velocity of 3 km/h north to south, we have;

The magnitude of her relative velocity to shore = √((Her relative velocity north to south)² + (The velocity of the English Channel east to west)²)

∴ The magnitude of her relative velocity to shore = √(3.5² + 2²) = (√65)/2 km/h

The magnitude of her relative velocity to shore ≈ 4.03 km/h