Analyzing Projectile Motion with Varying Angle and Acceleration in 2D

[JeffGlasgow]

Homework Statement

A moving point has a position function (P) and is given by 2D quantities where the (Y) axis is affected by gravity (9.8m/s/s) and (t) is in seconds.

X(t)=4t cos θ and Y(t)= 4t sin (θ)-5t^2



If θ = Pi /3 find the speed in directions after 10 seconds

Find the angle where maximum X direction = maximum Y direction

Find the time for maximum x direction = maximum Y direction

Find the acceleration after 2 seconds

Does the acceleration vary against time?




Relevant equations/notes

Equations of linear motion.

9.8m/s/s can be rounded to 10m/s/s for simplicity.

 

[CompuChip]

Hi Jeff, welcome to PF!
We have put the template that you haven't used in your post for a reason :) Maybe you can tell us what the "equations of linear motion" you mention are. I'm sure you already have some idea which one(s) to use?

 

[JeffGlasgow]

After a bit of research I'm under the impression I need to use the formulae

V= u + at

S = ut + 1/2 at^2

V^2 = u^2 + 2as

Also my error in that the position function should be (s) instead of (p)

 

[CompuChip]

Those formulas only hold for motion with constant acceleration a.
In your topic title you said "Differentiation with physics".
What does differentiation have to do with position and velocity?

 

[JeffGlasgow]

Our lecturer has just tried to make it relevant/more difficult due to the fact that we are doing an engineering course.

 

[CompuChip]

Actually I just realized that the formulas you gave are applicable in this case, so I'm a bit confused now whether your lecturer wants you to use differentiation or not.
I'm tempted to advise you to try both ways, but let's go for the first one first, since you have found those formulas.

What you should remember for 2D problems is that you need to consider the X and Y directions separately. So looking at

S = ut + 1/2 at^2

what are the initial velocity u_x and acceleration a_x in the X-direction? How about the Y-direction (u_y, a_y)?
Then what can you say about the formulas v_x, v_y for the velocity ?

 

[JeffGlasgow]

I have no idea where to start with this one, let me try and find some notes on this...

 

[CompuChip]

Look at the t's in the formula. The general expression for S(t) you gave is (something) * t + (something) * t².
Can you write the expression for X(t) and Y(t) in the same way? Then you can compare the "somethings" and you should be able to read off what u and (1/2)a are.

 

[JeffGlasgow]

For the y I get
S(t) = ut + 1/2 a t^2
Y(t) = 4t sin θ -5t^2 therefore I think that u =4 and a=-10 but I'm not sure where the sin theta comes from

And for the x I get
S(t) = ut + 1/2 a t^2
X(t) = 4t cosθ Therefore I think that u =4 again but I have nothing for a?! And I'm unsure where cos is relevant?