4. The benches of a gallery in a cricket stadium are 1 m
wide and 1 m high. A batsman strikes the ball at a level
one metre above the ground and hits a mammoth sixer.
The ball starts at 35 m/s at an angle of 53° with the
horizontal. The benches are perpendicular to the plane
of motion and the first bench is 110 m from the batsman.
On which bench will the ball hit ?
solve without using the equation of tragectory....
Answers
Answer :
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
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HOPE THIS MAY HELP YOU....
