Question

A body is moving on a circle of radius of 80 m with a speed 20 m/s which is decreasing at the rate of 5 m/$s^2$ at an instant. The angle made by its acceleration with its velocity is

Answer 1

Step 1, Given data and figure

Radius of the circle = 80 m

Speed = 20 m/s

Acceleration = 5 m/$s^2$

Step 2, Finding the angle made

According to the question, the speed of the object is decreasing so tangential acceleration will be opposite to the velocity vector.

Radial acceleration is 5 m/$s^2$

Tangential acceleration = $\frac{v^2}{R}=\frac{{20}^2}{80}=5$ m/$s^2$

From the above figure

$tan\theta =\frac{a_r}{a_c}=\frac{1}{1}=1$

So $\theta ={45}^0$

Now,

Angle made by net acceleration with the velocity

$\alpha ={90}^0+\theta ={90}^0+{45}^0={135}^0$

Hence the angle is ${135}^0$