An ant is crawling on a paper with a velocity $10 m . s^{- 1}$ in the direction shown in the figure. Now, you begin to pull the paper with velocity $10 m . s^{- 1}$ along x-axis as shown in the figure. Coordinate system has the origin fixed to the ground as shown in the figure. The initial position of ant is $(0, 0) .$ Select the correct alternative(s).

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Velocity of ant in ground frame is $(18 \hat{i} + 6 \hat{j}) m s^{- 1}$

Position vector of ant with respect to ground after $3 s$ is $(54 \hat{i} + 18 \hat{j}) m .$

In the ground frame, velocity vector of ant is time independent.

In the ground frame, velocity vector of ant is at an angle $θ < 37 °$ with x-axis.

answer is B, A, C, D.

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Detailed Solution

A) $\vec{v} = {\vec{v}}_{p} + {\vec{v}}_{a / p}$
$= 10 \hat{i} + (10 \cos 37 \hat{i} + 10 \sin 37 \hat{j}) = (18 \hat{i} + 6 \hat{j}) m / s$
B) $\vec{r} = \vec{v} t - (54 \hat{i} + 18 j) m$
C) $\tan α = \frac{v_{y}}{v_{x}} = \frac{6}{18} = \frac{1}{3} = 0.33$
$\tan 37 = \frac{3}{4} = 0.75 \Rightarrow α < 37 °$