A small boy is throwing a ball towards a wall 6 in front of him. He releases the ball at a height of 1.4 m from the ground. The ball bounces from the wall at a height of 3 m, rebounds from the ground and reaches the boys hand exactly at the point of release. Assuming the two bounces (one from the wall and the other from the ground) to be perfectly elastic, how far ahead of the boy did the ball bounce from the ground?

Options

A. `1.5m`
B. `2.5 m `
C. `3.5 m `
D. `4.5 m`

Answer

A

Explanation

`3 + (6 + x ) tan theta [1-(6 + x)/(12)]`
` 3= ((6 + x) (6-x) tan theta )/( 12)`
` 1.4 = x tan theta [1- (x)/(12)]`
` 1.4 = (x(12-x))/(12) tan theta `
` (30)/(14) = (36 -x^(2))/(12x -x^(2))`
` 360x - 30 x^(2) = 36 xx 14-14x^(2)`
` 16x^(2) - 360 x + 36 xx 14=0`
` x = (360 pm sqrt((360)^(2) - 4 xx 36 xx 14 xx 16))/(32)`
` x= (360 pm 312)/(32) = (48)/(32) = 1.5 `