Question

a body is moving on a circle of radius 80 metre with speed 20 metre per second which is decreasing at the rate of 5 metre per second square at the instant the angle made by its acceleration with its velocity is​

Answer 1

Hello Dear,

◆ 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°.

Thanks dear...