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A motor boat is racing towards North at ...

A motor boat is racing towards North at `25 km//h` and the water current in that region is `10 km//h` in the direction of `60^@` East of South. Find the resultant velocity of the boat.

A

11 km `h^(-1)`

B

22 km `h^(-1)`

C

33 km `h^(-1)`

D

44 km `h^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
The velocity of the motor boat and the velocity of the water current are represented by vectors `vecv_(b) and vecv_(c)` as shown in the figure.
Here, `theta = 180^(@) - 60^(@) = 120^(@)`
`v_(b) = 25 km h^(-1), v_(c) = 10 km h^(-1)`
`therefore` According to parallelogram law of vector addition, the magnitude of the resultant velocity fo the boat is
`vec_(R) = sqrt(v_(b)^(2) + v_(c)^(2) + 2v_(b)v_(c) cos 120^(@))`
` = sqrt((25)^(2) + (10)^(2) + 2(25)(10)((-1)/(2)))`
` = sqrt(625 + 100 - 250) = 22 kmh^(-1)`
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