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An inclined plane makes an angle theta0 ...

An inclined plane makes an angle `theta_0 = 30^@` with the horizontal. A particle is projected from this plane with a speed of `5 ms^-1` at an angle of elevation `beta = 30^@` with the horizontal as shown in (Fig. 5.53).
(a) Find the range of the particle on the plane when it strikes the plane.
(b) Find the range of the particle for `beta = 120^@`.
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Text Solution

Verified by Experts

(a) `prop' = theta_0 + beta = 60^@`
`R = (u^2)/(g cos^2 theta_0) [ sin (2 prop' - theta_0) + sin theta_0]`
=`(5^2)/(10 cos^2 30^@) [sin(2 xx 60^@ - 30^@) + sin 30^@] = 5 m`
(b) `prop + theta_0 + 120^@ = 180^@ rArr prop = 30^@`
`R = (u^2)/(g cos^2 theta_0) [sin( 2 prop + theta_0) - sin theta_0]`
=`(5^2)/(10 cos^2 30^@) [sin(2 xx 30^@ + 30^@) - sin 30^@] = 5//3 m`.
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