Question

A particle is projected from ground with velocity u at angle $θ$ from horizontal. Match the following two columns and mark the correct option from the codes given below.
Column I
(A) Average velocity between initial and final points
(B) Change in velocity between initial final points
(C) Change in velocity between initial and peak point
(D) Average velocity between initial and highest points
Column II
$(p) u \sin θ$
$(q) u \cos θ$
(r) zero
(s) None

Moderate

Solution

A) average velocity between initial and final point is
$v_{a v e} = \frac{R}{T} = \frac{u \cos θ T}{T} = U \cos θ$
B) change in velocity between initial and final point is
$g T = g \frac{2 u \sin θ}{g} = 2 u \sin θ$
C) change in velocity between initial and peak point is
$g \frac{T}{2} = u \sin θ$
D) average velocity between initial and peak point is
$\hat{i} u \cos θ + \frac{\hat{j} u \sin θ}{2}$

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