A man can reach thepoint directly opposite on the other bank of a river by swimming across the river in time t_1 and crosses the same distance in time t_2while swimming along the current. If the velocity of the man in still water is v and velocity of the watercurrent is u, find the ratio between t_1 and t_2.

A man can reach thepoint directly opposite on the other bank of a rive

1.	A man can reach thepoint directly opposite on the other bank of a river by swimming across the river in time t_1 and crosses the same distance in time t_2while swimming along the current. If the velocity of the man in still water is v and velocity of the watercurrent is u, find the ratio between t_1 and t_2.
Answer» Solution :Let the resultant velocity with which the man swims ACROSS the river ve w . Hence, `w=sqrt(v^2-u^2)` [Fig.2.51] and therefore , TIME REQUIRED to cross the river, `t_1=l/(sqrt(v^2-u^2)), ……(1)` where l is the width of the river. When the man swims in the direction of the CURRENT, the resultant velocity , w.=v+u and time required to cross the same distance, `t_2=l/(v+u) .....(2)` From(1) and (2) , `(t_1)/(t_2)=(v+u)/(sqrt(v^2-u^2))=(v+u)/(sqrt(v-u)*sqrt(v+u))=sqrt(v+u)/(v-u).`