Question

The benches of a Gallery in a cricket stadium are 1m wide and 1m high.A batsman hits the ball at a level one metre above the ground and hits a sixer .The ball starts at 35 ms^{​​​​​-1} at an angle of 53° with the horizontal . The benches are perpendicular to the plane of motion and the first bench is 110m from the batsman .On which bench will the ball hit?

Answer 1

The ball is bit at x =0 y =1 m.

slope of stair case of benches
= increase in y / increase in x
= height of step / width of step

The line joining the feet of the benches is = (y - 1) / (x - 110 ) = 1 / 1
= y = x - 109 - - equation 1

Equation of trajectory of cricket ball is :
x = u cos Ф t
t = x / u cos Ф

y = u sinФ t - 1/2 g t²
= x tan Ф - g x² / ( 2 u² cos² Ф )

y = 1.327 x - 9.8 * x² / (2 *35² * 0.362 )
= 1.327 x - 0.011 x² ---- equ 2

substitute y from equation 1

x - 109 =1.327 x - 0.011 x²

0.011 x² - 0.327 x - 109 = 0

Δ = 4.9
x = (0.327 +- 2.21 )/2*0.011

x = 115.32 meters

y at 115.32 m = 115.32 - 109 = 6.32 meters

So it is the 6th bench, as 1st bench is from 110m to 111m, 6 th bench is from 115 m to 116m.

Height y Back rest of the First bench is from 1 to 2 m ,
back rest of the sixth bench is 6 to 7 meters high

6th bench

hope it helps mate