A river is flowing along the east direction with a velocity of 10km/hr. A person heads towards north with a velocity of 2km/hr. what is the velocity of the person with respect to ground?
X = 10 km/h
Y = 2 km/h
V^2 = X^2 + Y^2 = 10^2 + 2^2 = 104
V = 10.20 m/s.
To find the velocity of the person with respect to the ground, we need to calculate the resultant velocity by considering the velocities of the river and the person.
Since the river is flowing eastward, we can consider its velocity as the x-component of the velocity.
Given:
Velocity of the river (Vr) = 10 km/hr (east)
Velocity of the person (Vp) = 2 km/hr (north)
To find the resultant velocity, we can use vector addition.
1. Convert the northward velocity to eastward direction:
Since the river is flowing east and the person is heading north, we need to convert the northward velocity into an eastward velocity. This can be done by considering the velocity vector as a right-angled triangle. The northward velocity is the perpendicular side, and the eastward velocity is the base of the triangle.
Using Pythagoras' theorem:
Velocity in eastward direction (Ve) = √(Vp^2 - Vr^2)
= √((2 km/hr)^2 - (10 km/hr)^2)
= √(4 km^2/hr^2 - 100 km^2/hr^2)
= √(-96 km^2/hr^2)
(The negative sign indicates that the velocity is in the opposite direction.)
2. Calculate the resultant velocity:
Velocity with respect to the ground (Vg) = √(Ve^2 + Vr^2)
= √((-96 km^2/hr^2) + (10 km/hr)^2)
= √(-96 km^2/hr^2 + 100 km^2/hr^2)
= √(4 km^2/hr^2)
= 2 km/hr
Therefore, the velocity of the person with respect to the ground is 2 km/hr, while the person is actually moving northward at a velocity of 2 km/hr.