# Sliding on ice

1. Mar 4, 2015

### PierceJ

1. The problem statement, all variables and given/known data
A 5.1 kg penguin runs onto a huge sheet of frictionless Antarctic ice. At t=0 it is at x=0 and y=0 with an initial velocity of 0.39 m/s along the positive x-axis. It slides while being pushed by the wind with a force of 0.53 N directed along the positive y-axis. Calculate the magnitude of the penguin's velocity at t = 11.81 s.

2. Relevant equations
x = V0xt
y = Voyt + 1/2ayt2

3. The attempt at a solution
The penguin is traveling in the positive x direction and being pushed up in the positive y direction, so I need to find the horizontal distance and the vertical distance and then I can get the magnitude and angle from that. So I start by setting up a drawing on a coordinate plane where the penguin starts at the origin and it goes 0.39(11.81)m in the x direction but I don't know what I should do for the y direction. Any help is greatly appreciated.

2. Mar 4, 2015

### Staff: Mentor

The question is asking for the velocity, not the distance. What is the acceleration in the y direction? If this acceleration continues for 11.81 sec, what is the velocity in the y direction after 11.81 sec. What is the resultant velocity?

Chet

3. Mar 4, 2015

### PierceJ

So the acceleration in the y direction is:
F = ma
0.53 = 5.1a
a = 0.1039m/s

So then I use V = V0 + at?
But what is the initial velocity in the y direction?

4. Mar 4, 2015

### Staff: Mentor

What do the words "with an initial velocity of 0.39 m/s along the positive x-axis" mean to you?

Chet

5. Mar 4, 2015

### PierceJ

It means that its moving 0.39 m/s horizontally.

6. Mar 4, 2015

### Staff: Mentor

It means that its initial velocity in the y direction is zero.

Chet

7. Mar 4, 2015

### PierceJ

Oh, I see now.
V = V0 + at
V = 1.288m/s

So then for the second part of the problem, I need to calculate the angle of that velocity.
So I have to find the displacement in x and then do the inverse cosine for the angle?

8. Mar 4, 2015

### Staff: Mentor

The direction of the displacement is not the same as the direction of the velocity. So why are you asking about the displacement? Do you know how to determine the magnitude of a vector if you know its two perpendicular components?

Chet

9. Mar 4, 2015

### PierceJ

Isnt it root(x2+y2)?

I'm asking because the question is asking me to find the angle.

10. Mar 4, 2015

### Staff: Mentor

The magnitude of the velocity is $\sqrt{(v_x)^2+(v_y)^2}$

The direction of the velocity is $\tan θ=\frac{v_y}{v_x}$

Note that there are no distances in these equations.

Chet

11. Mar 4, 2015

### PierceJ

So root((.39^2)+(1.288^2)) = 1.346

tan-1(1.346) = 53.38deg

12. Mar 4, 2015

### Staff: Mentor

The 1.346 is correct. The determination of the angle is not. See the equation for the angle again.

Chet

13. Mar 4, 2015

### PierceJ

Oh oops, read that wrong. Got it now, thanks a bunch!