In the arrangement shown, wedge is moving with constant velocity ( v 0 ) on a horizontal plane. A particle is projected horizontally from point A with velocity 10 m/s. If particle strkes the plane p

Question

In the arrangement shown, wedge is moving with constant velocity ( v 0 ​ ) on a horizontal plane. A particle is projected horizontally from point A with velocity 10 m/s. If particle strkes the plane perpendicularly after 2 sec of projection, then find the value of v 0 ​ in m/s.

TestHub · Accepted Answer

For a perpendicular strike, relative velocity along the incline is zero at $t = 2$ s.

At $t = 2$ s: $v_{x} = 10$ m/s, $v_{y} = - g t = - 20$ m/s.

Relative velocity: $(10 + v_{0}, - 20)$ m/s (wedge moves toward the particle).

Zero component along the incline: $(10 + v_{0}) cos 3 7^{\circ} = 20 sin 3 7^{\circ}$

$10 + v_{0} = 20 tan 3 7^{\circ} = 15$ , so $v_{0} = 5$ m/s.

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