Equation of trajectory of a particle moving in $x y$-plane is given by y=10 x - 2x2 (x and y are in meters). Assume acceleration of gravity as 10 m/s2 in negative y-direction. Choose correct statement(s).
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a
Maximum height of the particle is 12.5 m.
b
Range of the particle is x = 5 m.
c
At x = 2.25 m, particle is moving at an angle of 45o with x-axis.
d
Initially particle is projected at an angle of 53o.
answer is A.
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Detailed Solution
y=10x−2x2=10x1−x5Comparing it with y=xtanθ1−xR R=5m and tanθ=10u2sin2θg=5⇒ u22sinθcosθ=50⇒2u2101011101=50⇒ u2=25×10.1⇒ u=510.1m/sH=u2sin2θ2g=25(10.1)20100101=12.5mtanϕ=usinθ−gtucosθtanϕ=usinθ−gxucosθucosθ=u2sinθcosθ−gxu2cos2θ=1