# Projectile launched from an inclined plane strikes a wall horizontally

In summary, a projectile is projected perpendicularly to an inclined plane at a velocity of 50m/s. The projectile reaches a wall at a height of 2.25 seconds after it is projected.

## Homework Statement

There is an inclined plane which is inclined at an angle of 37° to the horizontal. A projectile is projected perpendicularly to the inclined plane at a velocity of 50m/s such that it strikes a wall kept at the foot of the inclined plane perpendicularly. Find the time taken to reach the wall.

## The Attempt at a Solution

I have correctly done this problem when we consider the x and y-axis vertically (wrt ground). The trick in this problem is that it has reached the maximum height just when it strikes the wall.
But, I am not getting the correct answer when I consider the x and y-axis along the inclined plane. My "faulty" method is described below:

As it reaches max height, y component of velocity decreases from 50 to 0. So, applying v=u+at in y-direction,
0=50+(-gcos37°)(t)
or, t=6.25 sec , which is 2.25 seconds more than what i got as the correct answer in my first method.
Please see where i went wrong.

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As it reaches max height, y component of velocity decreases from 50 to 0.
When the y-axis is perpendicular to the incline, is it correct to take the y-component of velocity to be zero at maximum height above the floor?

I can't find anything wrong. Please explain.

The projectile is moving perpendicular to the wall when it hits the wall. If a vector is perpendicular to the wall, it can't also be perpendicular to your y-axis. Therefore, the vector cannot have a zero y-component.

All right, got it.
So, basically it is sensible to take the y-axis parallel to the wall like in my first method, isn't it?
Is there any way to proceed from here?

All right, got it.
So, basically it is sensible to take the y-axis parallel to the wall like in my first method, isn't it?
Yes. I think it is easiest to have the y-axis parallel to the wall.
Is there any way to proceed from here?
You can work the problem with the y-axis chosen perpendicular to the incline. You will need to think about the relation between the x and y components of the velocity at the moment the projectile hits the wall.

Okay, I will try it.
@TSny Thank you very much.

You are welcome. Have fun with it.

## 1. What is a projectile launched from an inclined plane?

A projectile launched from an inclined plane is an object that is thrown or propelled from a ramp or sloped surface at an angle.

## 2. How does the angle of the inclined plane affect the projectile's trajectory?

The angle of the inclined plane affects the projectile's trajectory by changing the initial velocity and direction of the projectile. A steeper angle will result in a higher initial velocity, while a shallower angle will result in a lower initial velocity.

## 3. What factors determine the distance a projectile launched from an inclined plane will travel?

The distance a projectile launched from an inclined plane will travel is determined by the initial velocity, angle of the inclined plane, and the force of gravity. Air resistance and the mass of the projectile can also play a role.

## 4. How does the height of the inclined plane impact the projectile's motion?

The height of the inclined plane affects the projectile's motion by changing the potential energy of the projectile. A higher inclined plane will result in a higher potential energy, which can lead to a longer flight distance for the projectile.

## 5. What happens when a projectile launched from an inclined plane strikes a wall horizontally?

When a projectile launched from an inclined plane strikes a wall horizontally, it will bounce off the wall and continue to move in a straight line with the same initial velocity as before. This is due to the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another.

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