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Question

A ball projected from the ground at an angle of 45just clears a wall in front. If the point of projection is 4 m from the foot of the wall and the ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is :

A
4.4 m
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B
2.4 m
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C
3.6 m
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D
1.6 m
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Solution

The correct option is B 2.4 m


Here,
Range=4 m+6 m=10 m

As the ball is projected at an angle 45 to the horizontal,

Therefore, Range=4H

10=4HH=104=2.5 m

Maximum height, H=u2sin2θ2g

u2=H×2gsin2θ=2.5×2×10(12)2=100

u=100=10 ms1

From trajectory formula,

y=xtanθgx22u2cos2θ

So, the height of the wall PA is,

h=(OA) tanθg(OA)22u2cos2θ

h=(4×1)12×10×42102×(1/2)2

h=2.4 m

Hence, option (B) is correct.

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