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Grade: 11
        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?
5 years ago

Answers : (1)

Kevin Nash
askIITians Faculty
332 Points
							Sol. θ = 53°, so cos 53° = 3/5
Sec2 θ = 25/9 and tan θ = 4/3
Suppose the ball lands on nth bench
So, y = (n – 1)1  …(1) [ball starting point 1 m above ground]
Again y = x tan θ – (gx^2 Sec^2  θ)/(2u^2 ) [x = 110 + n – 1 = 110 + y]
⇒ y = (110 + y)(4/3) – (10 (110+y)^2 (25/9))/(2 x 〖35〗^2 )
⇒ 440/3 + 4/3 y - (25 (110+y )^2)/(18 x 〖35〗^2 )
From the equation, y can be calculated.
∴ y = 5
⇒ n – 1 = 5 ⇒ n = 6.
The ball will drop in sixth bench.

						
5 years ago
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