A man wants to reach point B on the opposite bank of a river flowing at a speed `4m//s` as shown in the figure. What minimum speed relative to water should the man have so that he can reach point B directly by swimming?

Options

A. `8 m//s`
B. `3.2 m//s`
C. `6.5 m//s`
D. `7sqrt(2) m//s`

Answer

B

Explanation

Note that speed of swimmer and angle both are unknown we have to determine function of speed and maximize it. Time taken for x-component of y-component of displacement are same.
`vec(v)_(S//R)=ucos thetahat(i)+usinthetahat(j)`
`vec(V)_(R//E)=upsilonhat(i)`
` vec(V)_(S//E)=(ucos theta +upsilon)hat(i)+u sin thetahat(j)`
`(theta0)/(ucostheta+upsilon)=(40)/(usintheta)`
`implies 3usintheta=4ucostheta+16`
`implies 3usintheta-4ucostheta=16`
`implies u = (16)/(3sintheta-4costheta)`
for `U_("min"),f(theta)=3sintheta-4costheta`should be maximum
`f(theta)_("max")=5`
`U_("min")=(16)/(5)m//s`