Question

A river is flowing at the rate of 6 km/hr . A swimmer swims across with a velocity of 9 km/hr with respect to the water .
The resultant velocity of the man will be in (km/hr )-
(a) (117)^1/2
(b) (340)^1/2
(c) (17)^1/2
(d) 3(40)^1/2


Please answer this and explain the solution.​

Answer 1

Answer:

Velocity of swimmer = 9kmph

Rate of flowing river = 6kmph

By drawing vector sum graph we will get the resultant velocity (with 6i^ and 9j^)

= √(6^2 + 9^2 )

= √117 kmph

Answer 2

Answer:

The resultant velocity of the man will be $(117)^{\frac{1}{2}}$

(a) is correct option.

Explanation:

Given that,

Velocity of river = 6 km/hr

Velocity of swimmer = 9 km/hr

We need to calculate the velocity of the man

Using Pythagorean theorem

$v_{r}^2=v_{river}^{2}+v_{swimmer}^{2}$

Where, $v_{river}$ = velocity of river

$v_{swimmer}$ = velocity of swimmer

Put the value into the formula

$v_{r}^2=(6)^2+(9)^2$

$v_{r}=\sqrt{(6)^2+(9)^2}$

$v_{r}=\sqrt{117}$

Hence, The resultant velocity of the man will be $(117)^{\frac{1}{2}}$