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Q.

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=xtan⁡θ1−xR                R=5m and tan⁡θ=10u2sin⁡2θg=5⇒ u22sin⁡θcos⁡θ=50⇒2u2101011101=50⇒ u2=25×10.1⇒ u=510.1m/sH=u2sin2⁡θ2g=25(10.1)20100101=12.5mtan⁡ϕ=usin⁡θ−gtucos⁡θtan⁡ϕ=usin⁡θ−gxucos⁡θucos⁡θ=u2sin⁡θcos⁡θ−gxu2cos2⁡θ=1
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