Question

A particle is projected from a horizontal floor with speed 10 m/s at an angle ${30}^0$ with the floor and striking the floor after sometime.State which is correct.

• A. Velocity of particle will be perpendicular to initial direction two seconds after projection.
• B. minimum speed of particle will be 5 m/sec.
• C. displacement of particle after half second will be 35/4 m.
• D. None of these.

Answer 1

The correct option is B minimum speed of particle will be 5 m/sec.

$T=\frac{2u\sin \theta }{g}=\frac{2\times 10\times \frac{1}{2}}{10}=1\sec .$

$\therefore$ option $\left(A\right)$ is incorrect$.$

$V_{min}=u\cos {30}^0$ $[$at peak$]$

$=5\sqrt{3}$ $\therefore$option $\left(B\right)$ is correct$.$

at $t=\frac{1}{2}$ sec$.$

$sx=4xt$

$=5\times \frac{1}{2}=\frac{5}{2}$

$10\cos {30}^0\times \frac{1}{2}=\frac{5\sqrt{3}}{2}$

$sy=uyt-\frac{1}{2}ay{t}^2$

$=10\sin {30}^0\times \frac{1}{2}-\frac{1}{2}\times 10\times \frac{1}{4}$

$=\frac{5}{2}-\frac{5}{4}=\frac{5}{4}$

$\therefore S=\sqrt{s{x}^2+s{y}^2}=\sqrt{\frac{75}{4}+\frac{25}{16}}=\frac{\sqrt{325}}{4}$

$\therefore$option $\left(C\right)$ is incorrect