Question

The ceiling of a long hall is ` 25 m` high. What is the maximum horizontal borizontal distance that a ball thrown with a speed of ` 40 ms^(-1)` can go without hitting the ceiling of the hall ?

Answer 1

Here, (u) be the velocity of projection of the ball. The ball will cover maximum horizontal distance when angle of projection with horizontal, `theta= 45^@`. Then` R_(max) = u^@ //g`
Here, ` u^2//g = 100 m`.
In order to study the motion of the ball along vertical direction, consider a point on the surface of earth as the origin and vetical upward direction as the positive direction of ` Y` axis . Taking motion of the ball along vertcal upward direction we have ` u_y = u, a_y =- u_y, =0 , t= ? y_0 =0 , y=?`
As, ` y= y_o + u_y t + 1/2 a_y t^2`
:. ` y =0 + u 9u// g) + 1/2 (-g) u^2//g^2 = u^2/g - 1/2 u^2 /g = ( 100)/ 2 = 50 m` [from (i)]` .