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[yrtherenonames]

Crap we have MX2 in 20 days and I can't do a 3unit question. Arnold/Arnold Diagnostic test 7 Question 9. I can set up the equations of motion but then I seem to have two unknowns in x/@. Please help.

 

[damo676767]

wanna give us the question?

 

[yrtherenonames]

A particle at the origin is projected at 30degrees at 60ms^-1
A particle 110m to the right is projected at angle @ at 50ms^-1
Given that these two particles collide, find
a)Angle of projection of 2nd particle
b)Distance from the origin at which they collide
c)Time of collision

 

[Trev]

a)
First particle:
y"=-g
y'=-gt + 60sin(pi/6)
y=(-gt²)/2 + 30t
Second particle:
y"=-g
y'=-gt + 50sinα
y=(-gt²)/2 + 50tsinα
Solving simultaneously:
30t = 50tsinα
sinα=3/5, blah.

b/c)
First particle:
x=60tcos(pi/6) = 30√3t
Second particle:
x=50tcosα + 110
Solving simultaneously:
30√3t = 50tcosα + 110 (since sinα=3/5 then cosα=4/5)
30√3t = 50t*(4/5) + 110 etc
∴ intersection when t = 3√3 +4 seconds.
%there4; intersection at x = 30√3(3√3+4) blah.
Think that's right

 

[robbo_145]

Second particle:
x=50tcosα + 110

it should be x= -50tcosα + 110 as it is traveling in the opposite direction to the first particle

 

[yrtherenonames]

Thanks people

 

[damo676767]

it never says that, we have no idea which direction it has been fired, there is 180 dgrees of posibility

 

[Trev]

sinα=3/5, angle alpha can lie in the first and second quadrants.

 

[yrtherenonames]

Sorry for any confusion, the two particles are definitely aimed towards each other; i.e. the one at the origin goes right, the one 110 metres away goes left

 

[Stefano]

This is a 4u question by the way, so don't freak out.

 

[yrtherenonames]

Surely it's harder 3unit? Could come up in Question 7 of MX1. There's nothin there that's not in the 3unit syllabus.