A ball is launched up a ramp with initial velocity vo At the

A ball is launched up a ramp with initial velocity v_o. At the time when the clock starts, the ball is near the bottom of the ramp and rolling up the ramp. Once the ball reaches the top, it rolls back down. For the graphs shown below, the horizontal axis represents time. The vertical axis is unspecified. Select the graph that corresponds to the correct quantity. Explain your reasoning. The x component of the ball\'s position The y component of the ball\'s position The x component of the ball\'s velocity The y-component of the ball\'s velocity The x-component of the ball\'s acceleration A cart rolls along a track at a constant speed. The cart has a funnel with a cocked spring. When the cart hits a certain point on the track, the hall is shot straight up in the air. Will the ball land In front of the funnel? In the funnel? Behind the funnel? You can\'t tell

Solution

For the given situation you need to consider the following:

1.) The ball starts off with velocity v and slows down to zero till it reaches the top with constant deceleration of gsin and then again, it starts acceleration downwards with velocity along the negative x axis and negative y axis.

2.) The displacement of the ball reaches as certain value for x and y axis and then reduces down to zero. Here it needs to be noted that the velocity decreases while going forward while it increases going backwards. As in, slope of the x vs t graph will decreases, approach zero and then increase in the negative direction.

3.) The acceleration remains contant and has negative component for the x direction as well as the y direction.

Now we have:

a.) X component of ball\'s position will increase to a certain value and then decrease: Plot H

b.) Y component will also follow a similar graph: H

c.) X component of ball\'s velocity decreases to zero and then increases in negative: A

d.) Y component of ball\'s velocity does same as x component: A

e.) X component of ball\'s acceleration remains constant and negative: B

2.) The ball when thrown upwards will have acceleration only in the vertical direction. As in its velocity along the X direction will not change and will remain same as that of cart.

Therefore, the horizontal distance it will cover will be same as the cart. Hence it will fall back in the funnel.