Projectile Motion Question (Different One) (1 Viewer)

[cutemouse]

Hi,

I have a question for time dilation. I think the answers may be wrong which is why I'm posting it here. Please do show me how you got to your answers etc. Thanks =D

A ball is thrown into air, leaving at an angle of 30 degrees to the horizontal at 6.0ms^-1. The maximum height reached by the ball is:

A 1.38 m
B 1.84 m
C 0.31 m
D 0.46 m

Thanks,

Jason

 

[Continuum]

It's D.

Resolve the 6ms^-1 at 30 degrees into components
u_y=6sin30

v_y²=u_y²+2a_yy
y=(v_y²-u_y²)/2a_y
y=[0-(6sin30)²]/[2(-9.8)]
y=0.46m

 

[cutemouse]

Oh okay, thank you...

Just wondering though,

I used the formulas below and got A, what did I do wrong?

Δy=u_yt+(1/2)a_yt²

To get t, I used t_up=(usinθ)/g

Thanks,

Jason

 

[Continuum]

You kind of used the wrong formula and the way you worked out the time is also wrong.

The formula you should use depends on what variables you have. If you look at the question, you see that you have u_y (vertical component of original vector), a_y (gravity is -9.8ms^-2) and v_y (since at maximum height, the vertical velocity is 0). You have no t (time) variable here and since the only equation without time is v_y²=u_y²+2a_yy, you'll use that equation.

The part where I said your time was wrong is because you can't just do initial speed over gravity. You actually have to use the equations of motion. Although you can work out time (albeit in a different way from yours) and find y from there, it takes very long.

So whenever you do a question, it might be easier if you just list the variables that you know and compare it with the equations of motion to see which one you can use.

 

[henry08]

So whenever you do a question, it might be easier if you just list the variables that you know

You should do that for every Physics calculation. Works well in maths as well.

 

[dolbinau]

Oh okay, thank you...

Just wondering though,

I used the formulas below and got A, what did I do wrong?

Δy=u_yt+(1/2)a_yt²

To get t, I used t_up=(usinθ)/g

Thanks,

Jason

Your value for T would have been correct, then substitute it into that formula (Vertical displacement) and you would have got the answer.


When vertical velocity = 0, T=0.3061

When T=0.3061 Y=(-4.9(0.3061^2))+6sin30(0.3061) = 0.459

I often use the extension methods - does this matter? (We technically have the same formulas)

 

[cutemouse]

Well with Physics projectile motion, you seperate the x and y components.

With Maths Ext 1 projectile motion, you just sub into formulas.

However, I think you can't get maximum marks if you use Maths Ext 1 projectile motion methods for Physics and vice versa. I'm not sure though, I'll ask one of the Physics teachers at school, as he's also a Maths teacher.

 

[dolbinau]

You mean the other way around (Physics we get the formulas).

But separating the x/y components in Maths extension is almost literally the formulas we get in Physics

i.e

horizontal acceleration= 0

Integrate =Horizontal Component = Velocity
Integrate = Horizontal Component(T)= Displacement

Which of course is the same as x=vt which we are given on the formula sheet.

I guess I'll write down the given formulas next to my working just in case.

 

[Continuum]

Your value for T would have been correct, then substitute it into that formula (Vertical displacement) and you would have got the answer.


When vertical velocity = 0, T=0.3061

When T=0.3061 Y=(-4.9(0.3061^2))+6sin30(0.3061) = 0.459

I often use the extension methods - does this matter? (We technically have the same formulas)

Lol, my bad, he's correct and I'm wrong in saying that your time would've been wrong. Sorry sorry, I should've actually checked your time beforehand.

 

[henry08]

With Maths Ext 1 projectile motion, you just sub into formulas.

I wish.

 

[cutemouse]

Obviously it's more than just subbing into formulae (duh!!!). But my point was that Mathematics doesn't split it into x and y component, and yes it's much harder as it involves differentiation, intergration, logs and all sorts of other crap.