Question

Ab body is moving on a circle of radius at metres with the speed of twenty meter per second which is decreasing at the rate five metre per second squad at an instant the angle made by its acceleration with its velocity is

Answer 1

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ANSWER ⏬

◆ Answer -

θ = 135°

◆ Explanation -

Tangential acceleration of body is given -

at = 5 m/s^2

Centripetal acceleration of body is -

ac = v^2 / r

ac = 20^2 / 80

ac = 5 m/s^2

Angle of resultant acceleration vector with radius,

tanθ1 = ac / at

tanθ1 = 5/5

tanθ1 = 1

θ1 = arctan(1)

θ1 = 45°

We know that velocity vector is perpendicular to radius at any instant of time.

θ2 = 90°

Hence, angle between acceleration and velocity is

θ = θ1 + θ2

θ = 45° + 90°

θ = 135°

Therefore, angle between acceleration and velocity of the body is 135°.

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