$v _1 \perp v _2$
$\therefore \quad v _1 \cdot v _2=0$
$\text { or }\left(u_1 \hat{ i }-g t \hat{ j }\right) \cdot\left(-u_2 \hat{ i }-g t \hat{ j }\right)=0$
$\therefore \quad g^2 t^2=u_1 u_2$
$\text { or }$
$t=\frac{\sqrt{u_1 u_2}}{g}$
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Figure: $Image$
$1.$ The speed of the block at point $B$ immediately after it strikes the second incline is
$(A)$ $\sqrt{60} \mathrm{~m} / \mathrm{s}$ $(B)$ $\sqrt{45} \mathrm{~m} / \mathrm{s}$
$(C)$ $\sqrt{30} \mathrm{~m} / \mathrm{s}$ $(D)$ $\sqrt{15} \mathrm{~m} / \mathrm{s}$
$2.$ The speed of the block at point $\mathrm{C}$, immediately before it leaves the second incline is
$(A)$ $\sqrt{120} \mathrm{~m} / \mathrm{s}$ $(B)$ $\sqrt{105} \mathrm{~m} / \mathrm{s}$
$(C)$ $\sqrt{90} \mathrm{~m} / \mathrm{s}$ $(D)$ $\sqrt{75} \mathrm{~m} / \mathrm{s}$
$3.$ If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point $B$, immediately after it strikes the second incline is
$(A)$ $\sqrt{30} \mathrm{~m} / \mathrm{s}$ $(B)$ $\sqrt{15} \mathrm{~m} / \mathrm{s}$
$(C)$ 0 $(D)$ $-\sqrt{15} \mathrm{~m} / \mathrm{s}$
Give the answer question $1,2$ and $3.$
$(A)$ $If \,m_1 > m_2$,
$(B)$ $If\, m_1 < m_2$,
$\text{zero}$
$\frac{1}{2}\text{Bl}\omega^2$
$\text{Bl}\omega ^2$
$2\text{B}\text{l}\omega^2$