Long Projectile Motion Question (1 Viewer)

[toknblackguy]

hi guys
all help appreciated
thanks

 

[香港!]

Hmm... maybe I'm sleepy or something... but I can't see any Projectile Motion Question, despite a "Long Projectile Motion Question" @_@

 

[toknblackguy]

attached image

 

[acmilan]

These arent projectile motion, but anyways:

(a)(i) A is initially at x = 2, with v = 0, so initial acceleration = -12 m/s/s, so it will move towards the left (or whichever direction you consider negative)

(ii)
d/dx (0.5v²) = -6x
0.5v² = -3x² + c
when t = 0, x = 2, v = 0, so c = 12
0.5v² = -3x² + 12
v² = -6x² + 24
v² = -6(x² - 4)

(iii) just look at the equations (graph if necessary)

(b)
(i) a = 6 - 6t²

when t = 0, v = 0, a = +6, so it will move in the positive direction

(ii)
dv/dx = 6 - 6t²
v = 6t - 2t³ + c
when t = 0, v = 0, c = 0
v = 6t - 2t³

(iii)
dx/dt = v = 6t - 2t³
x = 3t² - 0.5t⁴

(iv)

It's stationary when v = 0
6t - 2t³ = 0
t(6 - 2t²) = 0
t = -root(3), 0, root(3)

So at t = root(3) it will become stationary

 

[香港!]

o.o
But those questions aren't very projectile...

 

[toknblackguy]

Hmm... maybe I'm sleepy or something... but I can't see any Projectile Motion Question, despite a "Long Projectile Motion Question" @_@

hahaha
it seems im the one who's up too early and still sleepy

 

[toknblackguy]

These arent projectile motion, but anyways:

(a)(i) A is initially at x = 2, with v = 0, so initial acceleration = -12 m/s/s, so it will move towards the left (or whichever direction you consider negative)

(ii)
d/dx (0.5v²) = -6x
0.5v² = -3x² + c
when t = 0, x = 2, v = 0, so c = 12
0.5v² = -3x² + 12
v² = -6x² + 24
v² = -6(x² - 4)

(iii) just look at the equations (graph if necessary)

(b)
(i) a = 6 - 6t²

when t = 0, v = 0, a = +6, so it will move in the positive direction

(ii)
dv/dx = 6 - 6t²
v = 6t - 2t³ + c
when t = 0, v = 0, c = 0
v = 6t - 2t³

(iii)
dx/dt = v = 6t - 2t³
x = 3t² - 0.5t⁴

(iv)

It's stationary when v = 0
6t - 2t³ = 0
t(6 - 2t²) = 0
t = -root(3), 0, root(3)

So at t = root(3) it will become stationary

thanks alot acmilan!
you misread the question with part b and missed the c in biii but i got the idea
anyone got c?