A missile is projected with initial speed 42 m/s at an angle of 30 degrees...

A missile is projected with initial speed 42 m/s at an angle of 30 degrees above the horizontal. Ignoring air resistance, calculate the distance of the missile from the point of projection at the instant when it is moving downwards at an angle of 10 degrees to the horizontal.

Let the missile take t sec to reach its maximum height
=> by t = usinθ/g
=> t = 42 x sin30*/9.8
=>t = 2.14 sec
Let the missile after this point take t' sec to reach at a position where it make an angle of 10* downward to the horizon.
=> The vertival component at this point by tanθ = Vy/Vx [but Vx = Ux = constant = ucosθ]
=>tan10* = Vy/[42cos30*]
=>Vy = 6.41 m/s
=>By v = u + gt
=>6.41 = 0 + 9.8 x t'
=>t' = 0.65 sec
Thus by R = Ux x t
=>R = ucosθ x (t+t')
=>R = 42 x cos10* x (2.14+0.65)
=>R = 115.40 m

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