Question

A frog is swimming across a stream at a rate of 0.5m/s relative to the water. The current in the stream is 1m/s relative to the bank. Find the velocity of the frog relative to the bank. If the stream is 2m wide, how far downstream is the frog carried by the current?

Answer 1

let direction of the stream be along +ve x direction .

let unit vectors along +ve x and +ve y are i and j respectively.

velocity of water relative to bank=(1 i) m/s

velocity of frog relative to water=(0.5 j) m/s

then velocity of frog relative to bank=velocity of frog relative to water+velocity of water relative to bank

=(i+0.5*j) m/s

then magnitude of velocity=sqrt(1^2+0.5^2)=1.118 m/s

part b:

width of the stream is 2 m

velocity across the stream=0.5 m/s

then time taken =distance/speed=2/0.5=4 seconds

then distance travelled downstream=velocity along the stream*time=1*4=4 meter