Two balls with masses $m_{1}$ = 3 kg and $m_{2}$ = 5 kg have initial velocities $v_{1}$ = 5 m/s = $v_{2}$ in the directions as shown in figure. They collide at the origin. Find the velocity of the COM, 3sec before collision?

Q. The linear velocity of rotating body is given by

\to v = \to ω \times \to r .

\to ω = ˆ i - 2 ˆ j + 2 ˆ k

and

\to r = 4 ˆ j - 3 ˆ k

, then the magnitude of

\to v

is:

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A man is walking under an inclined mirror at a constant velocity V m/s along the X axis. If the mirror is inclined at an angle θ with the horizontal then what is the velocity of the image?

The correct option is D Vcos2θˆi+Vsin2θˆjAs shown in figure , V of O′(i.e, mirror image) is at a angle 2a wrt horizontal , if we resolve V of in x-axis and y-axis are Vcos2θ and Vsin2θ respectivey . V=Vcos2θi+Vsin2θj.

A man is walking under an inclined mirror at a constant velocity $V m / s$ along the X axis. If the mirror is inclined at an angle $θ$ with the horizontal then what is the velocity of the image?

The correct option is D $V c o s 2 θ ˆ i + V s i n 2 θ ˆ j$
As shown in figure , $V$ of $O^{'}$ (i.e, mirror image) is at a angle $2 a$ wrt horizontal ,
if we resolve $V$ of in x-axis and y-axis are $V c o s 2 θ$ and $V s i n 2 θ$ respectivey .
$V = V c o s 2 θ i + V s i n 2 θ j$ .