Physics Two Dimensional Motion Question 206
Question: Three points are located at the vertices of an equilateral triangle whose side equal to a. They all start moving simultaneously with velocity v constant in modulus, with first point heading continually for the second, the second for the third, and the third for the first. How soon will the points converge?
Options:
A) $ 3v/2a $
B)$ 2a/5v $
C) $ 5v/3a $
D)$ ~2a/3v $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] The motions of the points are sketched in the figure. As they start moving simultaneously symmetrically; they will meet at the centroid of the triangle. The velocity of any point towards centroid of triangle O $ \text{=},\text{v cos},\text{30}{}^\circ =\frac{\sqrt{3}\text{v}}{2}. $ And its displacement $ =\frac{a/2}{\cos 30{}^\circ }=\frac{a}{\sqrt{3}}. $ . Time taken to coverage the points $ =\frac{\text{displacement}}{\text{velocity}}=\frac{2a}{3v}. $
BETA
