Question

A particle moving with velocity of magnitude V changes its direction of motion by angle $\theta$ without change in speed. Find the (a) Magnitude of change of velocity. (b)Change in magnitude of velocity.

Answer 1

$\left(a\right)$ manitude of change in velocity =$\mid {\overrightarrow{v}}_f-{\overrightarrow{v}}_i\mid$

$\mid {\overrightarrow{v}}_f-{\overrightarrow{v}}_i\mid$=$\sqrt{V^2+V^2+2\times V\times V\times cos(180-\theta )}$

$\mid {\overrightarrow{v}}_f-{\overrightarrow{v}}_i$=$\sqrt{2V^2-2V^{2}cos\theta }$

$\mid {\overrightarrow{v}}_f-{\overrightarrow{v}}_i\mid$ =$\sqrt{2V^2(1-cos\theta )}$

using $1-cos\theta =2si{n}^2\frac{\theta }{2}$

$\mid {\overrightarrow{v}}_f-{\overrightarrow{v}}_i\mid$=$2Vsin\frac{\theta }{2}$

$\left(b\right)$ $\mid v_f\mid -\mid v_i\mid =V-V=0$