A swimmer can swim in stillwater at a rate 4 kilometre per hour. If he swims in a river flowing at 3 kilometre per hour and keeps his direction with respect to water perpendicular to the current,find his velocity city with respect to the ground
say the water is moving in x direction at 4 km/h
say we swim in y direction at 3 km/h
then our speed is sqrt (3^2+4^2) = 5 km/h
tan angle above x axis is
tan theta = 3/4 = .75
To find the swimmer's velocity with respect to the ground, we need to consider the vectors involved. The swimmer's velocity with respect to the ground is the sum of their velocity with respect to the water (taking into account the current) and the velocity of the water itself.
Given:
- Swimmer's velocity in still water: 4 km/h
- Velocity of the river current: 3 km/h
Since the swimmer is moving perpendicular to the current, we can treat their velocities as vectors and use the Pythagorean theorem to find the resultant velocity.
Using the Pythagorean theorem:
Resultant velocity^2 = (velocity in still water)^2 + (velocity of current)^2
Plugging in the given values:
Resultant velocity^2 = (4 km/h)^2 + (3 km/h)^2
Calculating:
Resultant velocity^2 = 16 km^2/h^2 + 9 km^2/h^2
Resultant velocity^2 = 25 km^2/h^2
Taking the square root of both sides to get the resultant velocity:
Resultant velocity = √(25 km^2/h^2)
Resultant velocity = 5 km/h
Therefore, the swimmer's velocity with respect to the ground is 5 km/h.