A particle has ⃗r(0) = (4 m)j and ⃗v(0) = (2 m/s)i.

Question

If its acceleration is constant and given by ⃗a = −(2 m/s2) (i +j), at what time t does the particle first cross the x axis?
Answer in units of s.

part 2. At what time t is the particle moving parallel to the y axis; that is, in the j direction?
Answer in units of s.

Answer 1

Let u = x direction velocity (i) and v = y direction (j) velocity

Xo = 0
Yo = 4

Uo = +2
Vo = 0

Ax = -2
Ay = -2

u = Uo + Ax t
u = 2 - 2 t

x = Xo + Uo t +(1/2) Ax t^2
x = 2 t - t^2

y = Yo + Vo t + (1/2) Ay t^2
y = 4 - t^2

so
y = 0 when t = 2

u = 0 when t = 1

Answer 2

Thank you very much.. i understand it...it crosses the x-axis when the y point is =o, and is parallel to the y- axis when the vector in the x direction aka the slope is = to 0 =]