NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Physics
- Chapter
- Motion in Two Dimensions
NTA Abhyas 2020 · Physics · Motion in Two Dimensions
A cyclist is moving with a constant acceleration of 1. 2ms^ - 2 on...
A cyclist is moving with a constant acceleration of on a straight track. A racer is moving on a circular path of the radius at a constant speed of . Find the magnitude of the velocity of racer which is measured by the cyclist has reached a speed of for the position represented in the figure.
Options
- A
- B
- C
- D
Correct answer
A.
Step-by-step solution
Let = actual velocity of cyclist along -axis
= the velocity of racer along tangent of circular path (shown in figure)
Hence {\overset{→}{v}}_{c} = 20\overset{^}{i}
{\overset{→}{v}}_{rc} = {V}_{r}cos {30}^{o}\overset{^}{j} + {V}_{r}sin {30}^{o}\overset{^}{i}
Or {\overset{→}{v}}_{r} = 15\cos 30\overset{^}{j} + 15\sin 30\overset{^}{i}
= \dfrac{15\sqrt{2}}{2}\overset{^}{j} + \dfrac{15}{2}\overset{^}{i}
= \dfrac{15\sqrt{3}}{2}\overset{^}{j} + \dfrac{15\sqrt{3}}{2}\overset{^}{j}
= - 12.5\overset{^}{i} + \dfrac{15\sqrt{3}}{2}\overset{^}{j}
= the velocity of racer along tangent of circular path (shown in figure)
Hence {\overset{→}{v}}_{c} = 20\overset{^}{i}
{\overset{→}{v}}_{rc} = {V}_{r}cos {30}^{o}\overset{^}{j} + {V}_{r}sin {30}^{o}\overset{^}{i}
Or {\overset{→}{v}}_{r} = 15\cos 30\overset{^}{j} + 15\sin 30\overset{^}{i}
= \dfrac{15\sqrt{2}}{2}\overset{^}{j} + \dfrac{15}{2}\overset{^}{i}
= \dfrac{15\sqrt{3}}{2}\overset{^}{j} + \dfrac{15\sqrt{3}}{2}\overset{^}{j}
= - 12.5\overset{^}{i} + \dfrac{15\sqrt{3}}{2}\overset{^}{j}