Question

A particle $A$ is moving along a straight line with velocity $3m/s$ and another particle $B$ has a velocity $5m/s$ at an angle ${30}^o$ to the path of $A$. Find the velocity of $B$ relative to $A$.

Answer 1

Given that,

Velocity of A $=3m/s$

Velocity of B $=5m/s$

Angle $\theta ={30}^0$

Now,

$V_{AB}=\sqrt{A^2+B^2+2AB\cos \theta }$

$V_{AB}=\sqrt{9+25+30\times \cos {30}^0}$

$V_{AB}=\sqrt{59.98}$

$V_{AB}=7.7m/s$

Now, the velocity of B relative to A

$V_{BA}=V_{AB}-V_A$

$V_{BA}=7.7-3$

$V_{BA}=4.7m/s$

of B relative to A is $4.7m/s$