# Solving for Initial Velocity Up a Plane: A Homework Problem

• joseg707
In summary, the problem involves a carton being given an initial speed of 3.0 m/s up a 22.0 degree plane with no friction. Using the equations F=ma and vf^2 = vi^2 + 2(a_x)(s), the acceleration in the x direction can be found using mg = Fncos(theta) and a_x = gsin(theta). The distance and time it takes to reach the maximum point can also be determined using these equations. To find the total time it takes for the carton to return to its starting point, the time it took to reach the highest point can be doubled.
joseg707

## Homework Statement

A carton is given an initial speed of 3.0 m/s up a 22.0 degree plane. a.) How far up the plane will it go? b.) How much time elapses before it returns to its starting point? Ignore friction.

F=ma

## The Attempt at a Solution

I have no clue. If someone could point me in the right direction and try to explain what's going on I would very much appreciate it.

I've been trying to figure it out. I know I'm supposed to break it into 2 equations, but I don't know how to express the 3.0 m/s velocity in the x equation.

$$\sum$$Fx=mg*sin$$\theta$$=max

$$\sum$$Fy=FN-mg*cos$$\theta$$=may=0

Is that right? If it is I still don't know where to go from here

Use the equation vf^2 = vi^2 + 2(a_x)(s).

But I don't know the time, nor the acceleration.

You have both the initial and final velocities so all you need right now is the acceleration in the x direction, which you can find by using mg = Fncos(theta) and a_x = gsin(theta).

Oh, ok. Now I get it. You put an (s) in the equation which threw me off. I found the distance and the time it took to reach the max point, but how do I get the total time? Should I just double the time it took to get to the highest point?

## What is the formula for calculating initial velocity up a plane?

The formula for calculating initial velocity up a plane is: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time elapsed.

## What information is needed to solve for initial velocity up a plane?

To solve for initial velocity up a plane, you will need to know the final velocity, acceleration, and time elapsed.

## Can initial velocity be negative when solving for initial velocity up a plane?

Yes, initial velocity can be negative when solving for initial velocity up a plane. This indicates that the object is moving in the opposite direction of the plane's incline.

## What are the units for initial velocity when solving for initial velocity up a plane?

The units for initial velocity when solving for initial velocity up a plane are typically meters per second (m/s).

## Are there any other factors that can affect initial velocity when solving for initial velocity up a plane?

Yes, factors such as air resistance and friction can affect the initial velocity when solving for initial velocity up a plane. These factors should be taken into consideration when solving the problem.

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