The benches of a gallery in a cricket stadium are 1 m wide and 1 m high. A batsman strikes the ball at a levl one metre above the ground and hits a mammoth sixer. The ball starts at 35 m/s at an angle of `53^0` with the horizontal. The benches are perpendicular to the plane of motion and the first bench is 110 m from the batsman.. On which benchk will theball hit?

Options

A. `4` th step
B. `5` th step
C. `6` th step
D. `7` th step

Answer

C

Explanation

Equation of ball,
`y=x tan theta-(gx^(2))/(2u^(2)cos^(2)theta` Substituting the values,
`y=1.33x-0.0113x^(2)`…(1)
Slope of line `MN` is `1` and it passes through point `(110 m,0)`.Hence the equation of this line can be written as , `y=x-110` ...(2)
Point of interrsecton of two curves is say `P`.Solving (1) and (2) we get positive value of `y` equal to `4.5m` i.e., `y_(P)=4.5`
Height of one step is `1 m`,Hence, the ball will collide somewhere between `y=4 m` and `y=5 m` which comes out to be `6th` step