Two particles are projected simultaneously from the same point, with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field acting vertically downwards. A frame of reference is fixed to one particle. The position vector of the other particle, as observed from this frame, is $\vec{r}$ . Which of the following statement is correct?

Moderate

A

$\vec{r}$ is a constant vector
B

$\vec{r}$ changes in magnitude as well as direction with time.
C

The magnitude of $\vec{r}$ increases linearly with time; its direction does not change.
D

The direction of $\vec{r}$ changes with time, its magnitude may or not change, depending on the angles of projection

Solution

A is fixed and B moves in the direction as shown in figure. w.r.t. ,A with constant velocity.
Direction of $\vec{r}$ remains same and magnitude changes with time' linearly
Here velocity of B w.r.t. A is constant because relative acceleration is zero.

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