In the following question, a statement of Assertion (A) is followed by a statement of Reason (R).
Assertion (A): If two particles, moving along straight line with constant velocities have to meet, the relative velocity must be along the line joining the two particles.
Reason (R): Relative motion means motion of one particle as viewed from the other particle.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true and the (R) is not the correct explanation of the (A)
3. (A) is true statement but (R) is false
4. Both (A) & (R) are false statements
View Answer
For two particles to meet, the relative velocity vector must align with the line joining them so that from one's frame, the other moves directly towards it.
Two particles are projected with same initial velocity one makes angle \(\theta\) with horizontal while other makes an angle \(\theta\) with vertical. If their common range is R then product of their time of flight is directly proportional to:
(1999)
1. R
2. \(R^{2}\)
3. \(\frac{1}{R}\)
4. \(R^{0}\)
View Answer
Concept: Time of flight for complementary angles and range formula.
Formula: \(T = (2u sin \alpha) / g\), \(R = (u^2 sin 2\alpha) / g\).
For angles \(\theta\) and \(90° - \theta\), times are \(T_1 = (2u sin \theta) / g\) and \(T_2 = (2u cos \theta) / g\).
Their product \(T_1 T_2 = (4u^2 sin \theta cos \theta) / g^2 = (2u^2 sin 2\theta) / g^2 = (2/g) R\). Thus, \(T_1 T_2 \propto R\).