A ball is thrown from ground level so as to just clear a wall 4 metres high at a distance of 4 metres and falls at a distance of 14 metres behind the wall. The magnitude velocity of projection of the ball will be:

Referring to (fig.) let P be a point on the trajectory whose co-ordinates are (4, 4). As the ball strikes the ground at a distance 14 metre from the wall, the range is 4 + 14 = 18 metre. The equation of trajectory isy=x tanθ−g2 x2u2cos2θ or y=xtan⁡θ1−gx2u2cos2⁡θ⋅tan⁡θ or y=xtan⁡θ1−g2u2xsin⁡θcos⁡θy=xtan⁡θ1−xR; where R is range here x=4,y=4 and R=18∴4=4tan⁡θ1−418=4tan⁡θ79 or tan⁡θ=97;sin⁡θ=9130 and cos⁡θ=7130 Again R=2gu2sin⁡θcos⁡θ ; in this equation substitute above obtained valuesrange R=(29.8)×u2×(9130)×(7130)   but R=18 ⇒u2 =18 ×  9.8  ×  130×   1302   ×    9    ×    7 =98    ×    137= 182, ⇒u =182Metre per second.