A particle is projected on an inclined plane with a speed `u` as shown in (Fig. 5.61). Find the range of the particle on the inclined plane.
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Options

A. `(2 u^2sqrt(3 + 1))/(3 g)`.
B. `(4u^2sqrt(3 - 1))/(9 g)`.
C. `(2 u^2sqrt(5 - 1))/(8 g)`.
D. `(2 u^2sqrt(3 - 1))/(3 g)`

Answer

D

Explanation

`R = (u^2)/(g cos^2 theta_0) [sin(2 prop + theta_0) - sin theta_0]`
where `theta_0 = 30^@ and prop = 45^@`
Then, `R = (u^2)/(g cos^2 30^@) [sin(2 xx 45^@ + 30^@)- sin30^(@)]`
=`(2 u^2sqrt(3 - 1))/(3 g)`.