Two Dimensional Kinematics probelms

[riken9]

Homework Statement

1. At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i - 4.0j) m/s2. At the instant the x coordinate of the particle is 15 m, what is the speed of the particle?

2. A particle starts from the origin at t = 0 with a velocity of 6.0 m/s and moves in the xy plane with a constant acceleration of (-2.0 + 4.0 ) m/s2. At the instant the particle achieves its maximum positive x coordinate, how far is it from the origin?

Homework Equations

rf = ri + vt + 1/2at^2
vf = vi + at

The Attempt at a Solution

1. rf = ri + vt + 1/2at^2
t = 2.25 [seconds]

vf = (9j) + [2i - 4j)t

Sub t into there and i get 4 m/s But the answer is: 10 m/s


2. v(initial)=6i m/s
v(final)=?
a= (-2i + 4j) m/s^2
starts at coordinate (0,0)
need to find max x point

rf = 6i + [-1i + 2j]t^2

vf = vi + at
How do i find t if i don't have final velocity? Answer is: 20m.

 

[TSny]

Hello, riken9. Welcome to PF!

For the first problem, your answer for the time is incorrect. Can you show your work so we can find the mistake?

For the second problem, there is not enough information given. Did they give you the direction of the velocity at t = 0? [EDIT: OK, it looks like from your work that the initial velocity is in the x direction. I think you will find things will be easier if you write out separate equations for the x and y components of the motion.]

 

[riken9]

for the first question rf = ri + vt + 1/2at^2, i did 15 = 0 + 9t - 2t^2 and got 2.25 seconds. I also tried 15 = 9j + [i - 2j]t^2 and got 1.27 seconds, which is also wrong.

And for the second problem i tried that still couldn't get it right.

 

[TSny]

for the first question rf = ri + vt + 1/2at^2, i did 15 = 0 + 9t - 2t^2

In the above equation you have mixed together x quantities (blue) and y quantities (red). Instead, write out equations for just the x component of motion and separate equations for the y component of motion. For example

x = x_i + v_xit + (1/2)a_xt²

y = y_i + v_yit + (1/2)a_yt²

or for velocity,

v_x = v_xi + a_xt

v_y = v_yi + a_yt

So, try using x = x_i + v_xit + (1/2)a_xt² to find the time for the first problem.