Question

A person swims at 135 degree to current of river to meet target on reaching opposite point. The ratio of persons velocity to river water velocity

Answer 1

Here is the answer :, (2)^1/2

Answer 2

ratio is $\sqrt{2} :1$

explanation:

$V_{SR}$ = velocity of swimmer with respect to river

$V_{R}$  = velocity of a river stream

• since it reaches opposite vertically, therefore velocity of swimmer in X- direction  with respect to ground is 'zero'.

• the basic formula we use is,

                      $V_{SR} cos$θ $= V_{R}$

                    $90^{0} +45^{0} = 135^{0}$

                       $90^{0} +$ θ  $= 135^{0}$

                               ∴θ$= 45^{0}$

• lets substitute values in our basic formula,

                  $V_{SR} cos$θ $= V_{R}$

                          $\frac{V_{SR}}{V_{R} } = \frac{1}{cos45^{0} } \\ \frac{V_{SR}}{V_{R} }= \frac{\sqrt{2} }{1^{} }$

  ∴ratio of persons velocity to river water velocity is $\sqrt{2} :1$