More confusion on projectile motion (1 Viewer)

[Jane Mao]

Sorry if this is dumb I literally haven’t been taught anything for mechanics. But regarding projectile motion can you use a definite integral when going form acceleration to velocity etc? Instead of letting t=0 and subbing in.

like this…

 

[SadCeliac]

Sorry if this is dumb I literally haven’t been taught anything for mechanics. But regarding projectile motion can you use a definite integral when going form acceleration to velocity etc? Instead of letting t=0 and subbing in.

like this…View attachment 39643

Yep, what you've done is correct

You can also use the same trick to make finding max height easier (E.g. by setting v=0 and y=H, where H is max height)

 

[Jane Mao]

Yep, what you've done is correct

You can also use the same trick to make finding max height easier (E.g. by setting v=0 and y=H, where H is max height)

Follow up question, why does it not work for when I'm going from y acceleration to y velocity? Like if I do this then i end up with an extra 10.

 

[SadCeliac]

Follow up question, why does it not work for when I'm going from y acceleration to y velocity? Like if I do this then i end up with an extra 10. View attachment 39645

Oh maybe I'm getting confused

This is my working for this type of stuff

 

[SadCeliac]

Follow up question, why does it not work for when I'm going from y acceleration to y velocity? Like if I do this then i end up with an extra 10. View attachment 39645

I think you actually can't use definite integral to find the six basic equations of motion, but you can find them really easily with +C when you draw out the initial velocity triangle (attached image) - note this is for a-->v, when you go v-->x your +C will be the point that you project from (usually the origin at 0,0)

 

[carrotsss]

Follow up question, why does it not work for when I'm going from y acceleration to y velocity? Like if I do this then i end up with an extra 10. View attachment 39645

you’re implying that t=vsin(theta), if you want to do it this way you have to do the limits when integrating both sides (ie the LHS will be y’ and vsin(theta) as limits and the RHS will be t and 0. The limits always have to correspond to what the pro numeral is actually equal to, and you always have to do it for both sides

 

[Jane Mao]

you’re implying that t=vsin(theta), if you want to do it this way you have to do the limits when integrating both sides (ie the LHS will be y’ and vsin(theta) as limits and the RHS will be t and 0. The limits always have to correspond to what the pro numeral is actually equal to, and you always have to do it for both sides

Ohh this makes so much sense. I get what I was doing wrong now lol I knew smth was off.