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The benches of a gallery in a cricket stadium are 1m 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 35m/s 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

The benches of a gallery in a cricket stadium are 1m 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 35m/s 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

Grade:12

1 Answers

Arun
25763 Points
2 years ago
given, @=53, cos53=3/5,sec53=25/9 and tan53=4/3 
let us suppose that ball lands on nth bench whose co ordinates are x and y, then y= (n-1) meter (1) 
as starting point of ball is one meter above horizontal level and x=110+(n-1) as first bench is 110 meters from batsman. 
then x=110+y (from eq.1) 
now by using y = xtan@-(gx^2sec2^2/2u^2) and substituting x= 110+y, we get y=5 
that implies n-1=5 
so n=6. so the ball will hit 6 th bench

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