Back to Directory
NEET PHYSICSEasy

A particle starting from the origin (0,0)(0,0) moves in a straight line in the (x,y)(x,y) plane. Its coordinates at a later time are (3,3)(\sqrt{3}, 3). The path of the particle makes an angle of __________ with the xx-axis:

A

30∘30^{\circ}

B

45∘45^{\circ}

C

60∘60^{\circ}

D

0∘0^{\circ}

Step-by-Step Solution

  1. Identify Coordinates: The particle moves from the origin O(0,0)O(0,0) to the point P(3,3)P(\sqrt{3}, 3). The displacement vector is r⃗=3i^+3j^\vec{r} = \sqrt{3}\hat{i} + 3\hat{j}.
  2. Formula for Direction: The angle θ\theta that a vector A⃗=Axi^+Ayj^\vec{A} = A_x\hat{i} + A_y\hat{j} makes with the positive xx-axis is given by tan⁡θ=AyAx\tan \theta = \frac{A_y}{A_x} .
  3. Substitute Values: Here, Ax=x=3A_x = x = \sqrt{3} and Ay=y=3A_y = y = 3. tan⁡θ=33=3\tan \theta = \frac{3}{\sqrt{3}} = \sqrt{3}
  4. Calculate Angle: We know that tan⁡60∘=3\tan 60^{\circ} = \sqrt{3}. Therefore, θ=60∘\theta = 60^{\circ}.
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started
Solved: PHYSICS Question for NEET | Sushrut