an aeroplane is flying in a horizontal circular path of circumference 10 km with a uniform speed of 100 km/hr. the change in its velocity in a quarter revolution with respect to original direction will be
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Velocity and Speed are two different concepts.
Speed is a Scalar. Velocity is a Vector.
Vectors have both magnitude and direction, unlike Scalars which only have magnitude. Change in either magnitude or direction or both , contributes to change in velocity i.e acceleration.
So when you talk about change in velocity , the change in direction comes into play.
In the above figure, V1, V2, V3, V4 are all different , as their direction is different even though their magnitudes are constant.
The speed is 100km/hr.
Circumference is 10km.
Change in velocity = V,final - V,initial
Let the plane start from angle zero. V,initial = 100km/hr (j).
( j is the unit vector in Y direction)
V, final = 100km/hr ( -i)
( i is the unit vector in X direction )
Since 1/4th revolution is 90 degrees of rotation, direction changes from Y to negative X.
So, Change in velocity = V,final - V,initial = 100(-i) -( 100(j)) km/hr.
= -100( i+ j ) km/hr.
The magnitude of vector xi + yj is sqrt( x^2 + y^2).
= 141 km/hr 90 degrees from the original direction.
Velocity and Speed are two different concepts.
Speed is a Scalar. Velocity is a Vector.
Vectors have both magnitude and direction, unlike Scalars which only have magnitude. Change in either magnitude or direction or both , contributes to change in velocity i.e acceleration.
So when you talk about change in velocity , the change in direction comes into play.
In the above figure, V1, V2, V3, V4 are all different , as their direction is different even though their magnitudes are constant.
The speed is 100km/hr.
Circumference is 10km.
Change in velocity = V,final - V,initial
Let the plane start from angle zero. V,initial = 100km/hr (j).
( j is the unit vector in Y direction)
V, final = 100km/hr ( -i)
( i is the unit vector in X direction )
Since 1/4th revolution is 90 degrees of rotation, direction changes from Y to negative X.
So, Change in velocity = V,final - V,initial = 100(-i) -( 100(j)) km/hr.
= -100( i+ j ) km/hr.
The magnitude of vector xi + yj is sqrt( x^2 + y^2).
= 141 km/hr 90 degrees from the original direction.
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