A motor boat is moving towards north at 25km/hr and rate of flow of water is 10km/hr along a direction of 60degree is east of south.Find the resultant velocity of the boat and also the direction in which it is moving?

Vb=25km/hr @ 90 deg. = Velocity of boat

Vw = 10km/hr @ 330 deg. = Velocity of
water.

X = hor. = 10cos330 = 8.66km/hr.

Y = ver. = 25 + 10sin330 = 20km/hr.

tanA = Y / X = 20 / 8.66 = 2.3094.
A = 66.6 deg.

R=X / cosA = 8.66 / cos66.6=21.8km/hr
@ 66.6 deg.=21.8km/hr @ 66.6 deg North
of East.

velocity of boats is 25m/s to north and velocity of water is 10m/s is 60 degree of east means the angles bw velocity of water and velocity of boats is 120 degree and by using triangle law of vector add. ans is 5 root 19

To find the resultant velocity of the boat, we need to consider both the velocity of the boat and the velocity of the water flow.

1. Draw a diagram: Draw a diagram indicating the given direction and magnitudes of the boat's velocity and water's velocity.

2. Resolve the velocities: Resolve the velocity of the water flow into its northward and eastward components. Since the angle is given as 60 degrees east of south, the northward component will be 10 × sin(60°), and the eastward component will be 10 × cos(60°).

Eastward component = 10 × cos(60°) = 10 × (1/2) = 5 km/hr
Northward component = 10 × sin(60°) = 10 × (√3/2) ≈ 8.66 km/hr

3. Calculate the resultant velocity: Add the northward component of the water velocity to the northward velocity of the boat since they are in the same direction. Subtract the eastward component of the water velocity from the northward velocity of the boat since they are in opposite directions.

Northward velocity = 25 km/hr + 8.66 km/hr = 33.66 km/hr
Eastward velocity = 5 km/hr

4. Find the magnitude and direction of the resultant velocity: Use the Pythagorean theorem to find the magnitude of the resultant velocity and the arctangent to find its direction.

Resultant velocity (magnitude) = √(Northward velocity² + Eastward velocity²)
= √(33.66² + 5²) ≈ 34.04 km/hr

Resultant velocity (direction) = arctan(Eastward velocity / Northward velocity)
= arctan(5 / 33.66) ≈ 8.53°

Therefore, the resultant velocity of the boat is approximately 34.04 km/hr, and it is moving in a direction approximately 8.53 degrees east of north.