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Question

The initial speed of an arrow shot from a bow, at an elevation of 30, is 15 ms1. Find its velocity when it hits the ground back.

A
7.5 m/sec at 60 clockwise from horizontal
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B
7.5 m/sec at 30 clockwise from horizontal
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C
15 m/sec at 30 clockwise from horizontal
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D
15 m/sec at 60 clockwise from horizontal
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Solution

The correct option is C 15 m/sec at 30 clockwise from horizontal

Given:
Initial speed u=15 m/s

Component along the xaxis

ux=15cos30

ux=1532 m/s

Component along yaxis

uy=15sin30=152 m/s

Time of flight is given by

T=2usinθg

T=2×15×(1/2)10=32 sec

Therefore, vx=ux=1532 m/s (ax=0)

and vy=uygt

vy=15210×32=152 m/s

v=v2y+v2x

v= (152)2+(1532)2=15 m/s

Now calculating the angle

tanθ=(152)(1532)=13

θ=300

Hence , option (A) is correct.

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