A ball is launched up a ramp with initial velocity Vo. At the time when the cloc

Question

A ball is launched up a ramp with initial velocity Vo. 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.... Help.... 1) A ball is launched up a ramp with initial velocity Vo. 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. Vo he graphs shown below, the horizontal axis represents time. The vertical axis is unspecified. Time Timt Tim Ti mt Timt Timt Timc Timt

Explanation / Answer

1. Here as the ball travells along the incline a component og acceleration due to gravity gx acts in the downward sense of the shown x-direction and a similar downward component gy acts in the shown y-direction.

(a), (b) for the both of these the position first increases and then decreases in a non-linear fashion because of the acceleration component (downward opening parabola for -ve acceleration) hence the answer is H.

(c) , (d) For both of these the velocity will first increase and then decrease (To be decided by the slope of the graph) in a linear fashion hence the option D.

(e) The value of the x-compoent of the acceleration would be constant and negative as I mentioned above hence the option B.

2. As the ball gets shot straight up in the air so by the time it reaches down the cart would have moved ahead and hence the ball would fall behind the cart.

3.

(a) For the stationary person the ball will have a forward compoent of the velocity (due to the moving car from which it fell down) and hence it's trajectory would be a parabola (projectile motion) so the answer is A.

(b) For the person on the car there is no forward component of velocity for the ball relative to him and hence the motion of the ball would be described by (In his frame) B.

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