A 4.0 x 101 kg wind sled is gliding East across a frozen lake at a constant speed of 12 m/s,

when a gust of wind from the southwest exerts a constant force of 1.0 x 102 N on its sails
for 3.0 s. With what velocity will the sled be moving after the wind has subsided?

p=mv=40•12 =480 kg•m/s.

F=100 N,
Δt=3 s.
Impulse = F•Δt=100•3=300 kg•m/s.
p is directed to the East
F•Δt=p1 is directed to the northeast.
p and p1 make the angle α=45º
Another angle in the parallelogram of momenta is [360-(2•45)]/2=135º
Use cosine law
p(net) =sqrt(p²+p1²-2p•p1•cos α) =
=sqrt(480²+ 300² -2•480•300•cos 135º)=
=sqrt(480²+ 300² +2•480•300•0.707)= 723.9 kg•m/s.
v=p(net)/m =723.9/40=18.1 m/s

To find the velocity of the sled after the wind has subsided, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Given:
- Mass of the sled (m) = 4.0 x 10^1 kg
- Initial velocity of the sled (u) = 12 m/s
- Force exerted by the wind (F) = 1.0 x 10^2 N
- Time for which the force is applied (t) = 3.0 s
- The direction of the gust of wind is from the southwest, which is at an angle of 45 degrees with the east direction.

First, we need to find the acceleration of the sled due to the force exerted by the wind. We can find this by using Newton's second law formula:

F = m * a

where F is the force, m is the mass, and a is the acceleration.

Rearranging the formula, we have:

a = F / m

Substituting the given values, we get:

a = (1.0 x 10^2 N) / (4.0 x 10^1 kg)

a = 2.5 m/s^2

So, the sled accelerates at a rate of 2.5 m/s^2 due to the force exerted by the wind.

Next, we need to determine how far the sled travels during the 3.0 seconds when the force is applied. We can use the formula:

S = ut + (1/2) * a * t^2

where S is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time.

Since the acceleration is constant, we can simplify the equation to:

S = ut + (1/2) * a * t^2

S = (12 m/s) * (3.0 s) + (1/2) * (2.5 m/s^2) * (3.0 s)^2

S = 36 m + 3.75 m

S = 39.75 m

Thus, during the 3.0 seconds when the force is applied, the sled travels a distance of 39.75 meters.

Finally, we need to find the sled's final velocity when the wind subsides. Since the force is no longer acting on the sled, it will continue to glide eastward at its constant speed. Therefore, the sled's velocity after the wind has subsided remains at 12 m/s.

So, the sled will be moving at a velocity of 12 m/s in the east direction after the wind has subsided.