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Question

Find the average velocity of a projectile between the instants it first crosses half the maximum height and then again does the same. It is projected with a speed u at an angle θ with the horizontal. (no need to calculate, just work it out mentally!).


A

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B

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C

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D

data insufficient

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Solution

The correct option is A


If we focus on the part of motion after the projectile has crossed half the projectile has crossed half the maximum height and has velocity v and makes angled with the x-axis.

Average velocity = total displacementtotal time

Total displacement is happening on the x-axis only

Which if I consider this part of motion as a new projectile will be its range I know range is nothing but Horizontal component of velocity × Time period

R = v cos α × T

Time period in this case will be 2 v sin αg

So R = v cos α × 2v sinαg

Now vavg = RT = v cosα × 2 v sinαg2v sinαg = v cosα = u cosθ.


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