Question

A particle is projected on a smooth fixed incline plane. Initial velocity of
particle is along inclined and at an angle ${53}^0$ with horizontal line AB. Then $[g=10m/s^2]$

• A. minimum speed of particle during it's motion on inclined is $15$ m/s.
• B. maximum height of particle from ground is $30$ m.
• C. particle returns back to line AB after $5$ sec.
• D. Range of particle along line AB is $120$ m.

Answer 1

Answer: (A), (D)

minimum speed of particle during it's motion on inclined is $15$ m/s.
Range of particle along line AB is $120$ m.

Along inclined; acceleration $a=gsin30=5m/s$
$v_{min}=25cos{53}^0=15m/s$
Along inclined, $H_{max}=\frac{{\left(25\right)}^{2}si{n}^2{53}^0}{2\times 5}=40m$

So, from ground $H_{max}=40sin{30}^0=20m$
$T=\frac{2u_x}{a}=\frac{2\times 20}{5}=8sec$
$R=\frac{2\left(u_x\right)\left(u_y\right)}{a}=$ $\frac{2\left(20\right)\left(15\right)}{5}=120m$