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Question Number 29118 by Tinkutara last updated on 04/Feb/18

Commented by Tinkutara last updated on 04/Feb/18
Use the values: e=3/5 m=7 kg M=15 kg u=30 m/s Theta=30°
Commented by Tinkutara last updated on 04/Feb/18
Thank you very much Sir! I got the answer.
Commented by ajfour last updated on 04/Feb/18

Commented by ajfour last updated on 04/Feb/18

$v + V \sin θ = e u \sin θ$ $(a l o n g n o r m a l t o i n c l i n e o f w e d g e)$ $M V + m u \cos^{2} θ - m v \sin θ = m u$ $(m o m e n t u m c o n s e r v a t i o n$ $a l o n g h o r i z o n t a l)$ $\Rightarrow M V - m (e u \sin θ - V \sin θ) \sin θ$ $= m u \sin^{2} θ$ $V = \frac{m u (1 + e) \sin^{2} θ}{M + m \sin^{2} θ} .$
Commented by mrW2 last updated on 04/Feb/18

$e_{⊥} = e = \frac{V \sin θ + v}{u \sin θ}$ $\Rightarrow V \sin θ + v = e u \sin θ$ $e_{/ /} = 1 = \frac{v_{/ /} - V \cos θ}{u \cos θ} (*)$ $\Rightarrow v_{/ /} = (u + V) \cos θ \neq u \cos θ$ $a s s u m e p a r a l l e l r e s t i t u t i o n c o e f . = 1$
Commented by ajfour last updated on 04/Feb/18

$b a l l d i d n o t r e c e i v e a n y i m p u l s e$ $p a r a l l e l t o i n c l i n e, t h e w e d g e$ $d i d r e c e i e v e a n i m p u l s i v e$ $c o m p o n e n t f r o m g r o u n d,$ $p a r a l l e l t o i t s i n c l i n e, s o$ $v_{/ /} o f b a l l = u \cos θ$ $a n d n o t v_{/ /} - V \cos θ = u \cos θ,$ $S i r!$
	Answered by ajfour last updated on 04/Feb/18

	$V_{M} = 5.04 m / s .$
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