There is something missing from your equation for y(t)atomB said:
Yes, changing the angle of the ramp will affect the distance the ball travels. The steeper the angle of the ramp, the farther the ball will travel. This is due to the influence of gravity and the increased potential energy of the ball at a higher angle.
The height of the ramp and the speed of the ball are directly proportional. This means that as the height of the ramp increases, the speed of the ball also increases. This is because a higher ramp provides more potential energy for the ball to convert into kinetic energy, resulting in a faster speed.
The weight of the ball does not have a significant impact on its trajectory when it hits the ramp. As long as the ball has enough momentum to reach the top of the ramp, it will follow the same path regardless of its weight. However, a heavier ball may roll farther once it reaches the end of the ramp due to its increased mass and momentum.
If the ramp is not perfectly straight, the ball's trajectory will be affected. This is due to the force of gravity pulling the ball towards the center of the earth, causing it to follow a curved path. The degree of curvature will depend on the angle and location of the curve in the ramp.
Yes, the type of surface on the ramp can affect the speed of the ball. A smoother surface will result in less friction, allowing the ball to travel faster. On the other hand, a rougher surface will create more friction, slowing down the ball's speed. Other factors such as the material and shape of the surface can also impact the ball's speed.