Question

A boat crosses a river with a velocity of 8 km/hr. If the resulting velocity of boat is 10 km/hr, then the velocity of river water is?
1) 4 km/hr
2) 6 km/hr
3) 8 km/hr
4) 10 km/hr

Answer 1

Hint: Velocity of an object is defined with magnitude and direction, where direction of the moving object plays an important role. Here,Velocity of boat and velocity of water would be perpendicular so Pythagoras theorem can be applied.

Complete answer:
Let Velocity of boat crossing river be \[{V_1}\]and the Velocity of flowing water be \[{V_2}\]
Velocity of boat crossing river = 8km/hr.
Velocity of flowing water = \[{V_2}\] km/hr.
Resultant velocity of boat = 10 km/hr.

By Vector Law of Addition,
\[V = \sqrt {V_1^2 + V_2^2 + 2{V_1}{V_2}\cos \theta } \]
But here since Velocity of boat and velocity of water are perpendicular

So the angle will be ninety degree which makes , \[\cos {90^o} = 0\]
\[\therefore \]\[V = \sqrt {V_1^2 + V_2^2} \]
\[\therefore \]\[10 = \sqrt {{8^2} + V_2^2} \]
\[\therefore \]\[100 = 64 + V_2^2\]
\[\therefore \]\[{V_2} = 6\]km/hr

Hence, the answer is b) 6 km/hr.

Note: In this as the velocities are squared, so the direction that is with the negative sign does not matter. We have to be careful while choosing the answer.