Question

A small ball is projected along the surface of a smooth inclined plane with speed $10{ms}^{-1}$ along the direction shown at $t=0$. The point of projection is origin, $z-$axis is along vertical. The acceleration due to gravity is $10{ms}^{-2}$. Column I lists the values of certain parameters related to motion of ball and Column II lists different time instants Match appropriately.

Answer 1

R.E.F image

$a=$ acceleration down the in line

$a=-gsin{37}^{\circ }$

$=-6m/s^2$

$U_a=10cos{37}^{\circ }=8m/s$

$U_b=10sin{37}^{\circ }=6m/s$

(i) $s=2.25$ (tron x $-$ axis)

$s=Ubt+\frac{1}{2}a{t}^2$

$2.25=6t-\frac{1}{2}\times 6\times t^2$

So $t=0.5,1.5$ second

So option a,b Answer

(ii) Speed is minimum when $U_b=0$

$V=U_b+at$

$0=b-bt$

$t=1$ second

So Option B answer

(iii) At $t=0$ velocity moles ${37}^{\circ }$

with x $-$ axis

Also at $t=T$ (Time of flight)

again velocity will molar ${37}^{\circ }$

with x $-$ axis

$V=U+at$

$-U_b=U_a+aT(att=T)$

$(V=-U_b)$

$-b=b-6t$

$6t=12$

$t=2$ second

So option D answer.