A 5.70 kg penguin runs onto a huge sheet of frictionless Arctic ice. At t=0 it is at x=0 and y=0 with an initial velocity of 0.35 m/s along the positive x-axis. It slides while being pushed by the wind with a force of 0.45 N directed along the positive y-axis. Calculate the magnitude of the penguin's velocity at t = 10.73 s.

To calculate the magnitude of the penguin's velocity at t = 10.73 s, we will use Newton's second law of motion and the principles of vector addition.

First, let's find the acceleration of the penguin. We know that the net force acting on the penguin is the force by the wind, which is 0.45 N along the positive y-axis.

Using Newton's second law of motion:
F = ma

where F is the force, m is the mass, and a is the acceleration, we can rearrange the equation to solve for acceleration:
a = F / m

Given that the mass of the penguin is 5.70 kg and the force is 0.45 N, we can substitute these values into the equation to find the acceleration:
a = 0.45 N / 5.70 kg

Calculating this, we find that the acceleration of the penguin is approximately 0.0789 m/s^2.

Next, we need to find the penguin's velocity at t = 10.73 s. We can use the following kinematic equation to do this:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Given that the initial velocity (u) is 0.35 m/s, the acceleration (a) is 0.0789 m/s^2, and the time (t) is 10.73 s, we can substitute these values into the equation and solve for the final velocity (v):
v = 0.35 m/s + (0.0789 m/s^2) * 10.73 s

Calculating this, we find that the magnitude of the penguin's velocity at t = 10.73 s is approximately 1.199 m/s.

the velocity in the x-direction is constant

the penguin is accelerated in the y-direction by the wind

a = f / m = .45 / 5.7

v = a * t

the x-velocity and y-velocity add as vectors to give the net velocity
(vx)^2 + (vy)^2 = v^2