# Time in Air for Ball Rolling Down a Ramp

• bwagner
In summary, the conversation discusses finding the amount of time a ball is in the air after leaving a declining ramp. Two approaches are suggested - finding the average velocity or equating potential and kinetic energy. The velocity as the ball leaves the ramp is twice the calculated velocity of distance over time due to uniform acceleration. The angle of the ramp must also be known to resolve the velocity in the x direction.
bwagner

## Homework Statement

A ball is placed 0.700m from the end of a declining ramp and rolls down the ramp in 0.750s. The marble is also 0.175m from the horizontal. The ball hits a mark on the floor that is 1.70m from the bottom of the ramp on the x-axis. What mount of time is the ball in the air after leaving the ramp?

## The Attempt at a Solution

Can't find initial velocity.

Seems like a couple of approaches are available: one is to simply find the average velocity from the length of the ramp anf the time spent. Since acceleration is uniform the velocity as it leaves the ramp is twice that (initial velocity is zero).

The other is to equate potantial energy loss with kinetic energy gain while on the ramp.

In other words, mgh=1/2mv^2

From there you need to know the angle of the ramp. Then resolve the velocity in the x direction. This help?

The velocity,as it leaves the ramp, is twice what? The calculated velocity of distance/time?

Yep. The reason is that the acceleration is uniform. Otherwise this isn't true.

## 1. What is a ball down a ramp projectile?

A ball down a ramp projectile is a scientific concept that involves a ball rolling down a ramp and becoming a projectile once it leaves the ramp. This means that the ball will follow a curved path in the air due to the forces acting on it.

## 2. What factors affect the trajectory of a ball down a ramp projectile?

The trajectory of a ball down a ramp projectile is affected by several factors, including the angle of the ramp, the initial velocity of the ball, the mass of the ball, and the presence of air resistance.

## 3. How does the angle of the ramp affect the distance traveled by the ball?

The angle of the ramp affects the distance traveled by the ball because it determines the initial velocity of the ball. A steeper ramp will give the ball a higher initial velocity, resulting in a longer distance traveled.

## 4. What is the relationship between the initial velocity and the range of a ball down a ramp projectile?

The initial velocity and the range of a ball down a ramp projectile have a direct relationship. This means that as the initial velocity increases, the range also increases. However, this relationship is not linear and is affected by other factors such as air resistance.

## 5. How does air resistance affect the motion of a ball down a ramp projectile?

Air resistance can significantly affect the motion of a ball down a ramp projectile. It can slow down the ball's motion, causing it to cover a shorter distance and have a lower peak height. This effect is more pronounced for lighter and smoother balls.

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