Projectile motion on an incline

[boreal fjord]

A body is projected up with speed v along the line of greatest slope of an inclined plane with inclination "A". If body collides elastically perpendicular to the plane, find the time after which the body passes through its point of projection.

[hexed tendon]

1. Do not ping the Moderators, unless someone is breaking the rules.
2. Do not ping the Helper Moderators, unless there is a conflict between helpers.
3. Do not ping other members randomly for help.
4. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
5. Wait patiently for a helper to come along.
6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[boreal fjord]

When the body collides with the plane, it will only have the vertical component of velocity.

As the collision is elastic, this vertical velocity just flips it direction

That means, the object shouldn't reach its original point of projection?

This is what I mean.

Do, we have to consider the fact that the object will roll down the incline to original point (and add this time)

T1= time to go up the incline
T2= for vertically up and down motion
T3= Rolling down

T=T1+T2+T3

[shrewd sand]

why not

[boreal fjord]

Yes, it will roll down?

[shrewd sand]

shouldn’t it bounce back to like exactly where it started or something

[boreal fjord]

How? It landed perpendiculary to the surface of incline

So, at collision, you only have Vy

[shrewd sand]

yeah so it should go back up

[shrewd sand]

is y the direction perpendicular to the incline or the vertical direction

[boreal fjord]

Perpendicular to incline

[boreal fjord]

Like here

[shrewd sand]

yeah ok

the body should literally just retrace its path back to the start though

like the velocity gets negated

[boreal fjord]

That's what the solutions says

But, it doesn't make sense to me

[shrewd sand]

why not

[boreal fjord]

The fact that Vy reverses direction at contact but Vx=0 so net velocity is in Y direction

[shrewd sand]

so the direction is completely flipped right

[boreal fjord]

Only in Y-axis!

As Vx=0 so there is nothing to flip!

[shrewd sand]

it’s 0 in the X-axis

[shrewd sand]

yeah but 0 flipped is 0

[boreal fjord]

Yeah, so vertically up

[shrewd sand]

so it’s completely flipped

[boreal fjord]

In Y axis?

[shrewd sand]

in both axes?????

ok wait can I tell you how I’m imagining the problem

[boreal fjord]

It had no velocity in X-axis, so what is gonna flip

[shrewd sand]

how are you missing my point so hard

if I flip 0 then it is still 0

[boreal fjord]

Can you show a diagram?

[shrewd sand]

so if the velocity was (0, v) before then it’s (0, -v) now

[shrewd sand]

which is the negative of what it was before in both axes

[boreal fjord]

Yes and the direction ofnet velocity is in +Y axis only

[boreal fjord]

I see

0i-vj flips to 0i+vj

[shrewd sand]

purple line is the velocity before collision, blue is after

they are parallel have the same magnitude and are in opposite directions

ok suppose you imagine there’s a video of the ball’s path from where it starts to where it hits the incline

[shrewd sand]

and then as soon as it hits the incline, you play the video backwards

what does that do? it reverses the velocity and doesn’t change the acceleration

[boreal fjord]

Alright, I can imagine that.

Okay, so it retraces its path

so total time=2T where T is the time to go up

[shrewd sand]

should remain to find that ig

your original q was kinda vague there’s like a gazillion variables

not sure if it’s just me who’s reading it wrong

[boreal fjord]

Yeah lmao

$T=\frac{2v}{g \sqrt{1+3sin^2A}}$

I found out T

[slender talon]

Agent Krasnov

[boreal fjord]

So $2T=\frac{4v}{g \sqrt{1+3sin^2A}}$

[slender talon]

Agent Krasnov

[boreal fjord]

Is the final answer

[shrewd sand]

ooh nice

yeah that’d do it lol

[boreal fjord]

Anyways thanks!

I had a massive conceptual error.

[shrewd sand]

np :D

[boreal fjord]

+close

[tribal relic]

Please thank your Helpers before closing!

Please thank the helpers who assisted you by clicking the buttons below. You can thank each helper only once. Once you're done, click "Close Post" to close this thread.

[tribal relic]

Thank you for your feedback! lil’ gabbie has been awarded 1 . They now have 27 . They have 3 daily left for today.

[shrewd sand]

:00000

yooo