From a point on the ground at a distance `a` from the foot of a pole, a ball is thrown at an angle of `45^@`, which just touches the top of the pole and strikes the ground at a distance of `b`, on the outer side of it. Find the height of the pole.

Options

A. `(ab)/(a-b)`
B. `(ab)/(a+b)`
C. `(2ab)/(a+b)`
D. `(ab)/(a+2b)`

Answer

B

Explanation

Let `h` be the height of the pole.We have `y=x tan alpha(1-x/r)` Since top of pole, lie on curve.`(l)`,
`h=a tan 45^(@)(1-a/(a+b))=a[(a+b-a)/(a+b)]=(ab)/(a+b)`