Physics Two Dimensional Motion Question 77

Question: A particle is projected from the ground with an initial speed of $ v $ at an angle $ \theta $ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

Options:

A) $ \frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta } $ B) $ \frac{v}{2}\sqrt{1+2{{\cos }^{2}}\theta } $ C) $ \frac{v}{2}\sqrt{1+3{{\cos }^{2}}\theta } $ D) $ v,\cos ,\theta $

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Answer:

Correct Answer: C

Solution:

[c] Average velocity $ =\frac{Displacement}{Time} $

$ =\frac{\sqrt{H^{2}+R^{2}/4}}{T/2} $ Putting the required values, we get $ v _{av}=\frac{v}{2}\sqrt{1+3{{\cos }^{2}}\theta } $