Titled reference frame, N2L with position and velocity

learningphysics

Yes. Now use the values we've calculated for v0 and a for this problem... for the x- direction... and the y-direction...

Oblio

dx = vocos[tex]\vartheta[/tex]t + (1/2)(-g)t^2sin[tex]\phi[/tex]

dy = vosin[tex]\vartheta[/tex]t + (1/2)(-g)t^2cos[tex]\phi[/tex]

Oblio

i have a feeling this is wrong for dy....

learningphysics

Looks right to me. So now you want to find the range...

Oblio

range?

learningphysics

the question asks for the range...

Oblio

which is really just the displacement up the plane?

learningphysics

yes, maximum displacement... the object is thrown at an angle, then hits the incline eventually... the displacement up the plane when it hits is the range...

Oblio

is this the same kinematics equation?

learningphysics

use these equations to find dx when dy = 0... that gives the range.

Oblio

solve for...... vo? and insert into dx?

learningphysics

no, you want to eliminate t... so solve for t and substitute into dx.

Oblio

without simplifying yet..

dx = vocos (theta) (vosin (theta) / (-1/2)gsin(phi)) + (1/2)(-g)cos(phi)((vosin(theta)/(-1/2)gsin)^2)

ya?

learningphysics

hmm... close but some mistakes... can you post what you got for t?

Oblio

t = vosin(theta) / (-1/2)gsin(phi)

learningphysics

setting dy = 0, and solving for t will give you something different... it should be cos(phi) and the - shouldn't be there.

Oblio

oops! little pen and ink mistake over here..

t = vosin(theta) / (1/2)gcos(phi)
yep!