acceleration at an angle??????

Question

if something accelerates at an angle, say 3m/s^2 at 30 degrees above horizon, does that mean it accelerate cos(30)3 horizonally and sin(30)3 vertically?

Answer 1

Yes. You can figure that out by considering the velocity vectors.

Given the numbers in your example, and assuming we start from rest:

At any given time t, the (diagonal) velocity will be:

V = (3m/s²)•t

So the horizontal & vertical components of V will be:

Vx = Vcos(30) = (3m/s²)cos(30)•t
Vy = Vsin(30) = (3m/s²)sin(30)•t

Now, the horizontal component of the acceleration is (by definition) the rate at which the horizontal velocity is changing. That is:

Ax = Vx/t

Combining that with the previous equation we get:

Ax = Vx/t = (3m/s²)cos(30)

And a similar thing for the vertical component.

Answer 2

Yeah, it is important to remember that velocity and acceleration are vectors. The both have x and y coordinates.

And yes those are the correct answers.

Answer 3

Yes, your answers are correct. Acceleration is a vector, so it has an x component and a y component.