A small cart A starts moving on a horizontal surface, assumed to be $$X-Y$$ plane along a straight line parallel to $$X-axis$$ (see$$ $$figure) with a constant acceleration of $$4$$ $$m/s2$$. Initially it is located on the positive $$Y-axis$$ at a distance $$9$$ m from origin. At the instant the cart starts moving, a ball is rolled along the surface from the origin in a direction making an angle $$45o$$ with the $$X-axis$$. The ball moves without friction at a constant velocity and hits the cart. Find the speed of the ball (in$$ $$m/s).

Question

Infinity Learn · Accepted Answer

Let us consider the motion of the ball from frame of reference of the cart. In this frame the ball follows a parabolic path. In this frame it has a constant acceleration of $$4$$ $$m/s2$$ in negative $$X-direction$$. From frame of reference of the cart, the motion of the ball can be considered as projectile motion, here we can write  Range $$=OA=u2sin$$⁡$$2$$θa⇒$$9=u2sin$$⁡$$90$$∘$$4$$⇒$$u=6m/s$$

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App