A body is moving on a circle of radius 80m with a speed 20m/s which is decreasing at the rate of 5m/s2 at an istant. What is the angle made by its acceleration with its velocity?
a) 45°
b) 90°
c) 135°
d) 0°
Answers
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°.
Answer:
135°
Explanation:
tangential acceleration= 5m/s^2
centripetal acceleration=v^2/r
ac= 20^2/80
= 400/80
=5m/s^2
tan anlge1= 5/5=1
tan anlge1=45°
we know velocity vector is perpendicular to acceleration = 90°
angle. made by its acceleration with its velocity is =90+45° = 135°