A model sailboat is slowly sailing west across a a pond at.33m/s. a gust of wind blowing at 28 degrees south of west gives the sailboat a constant acceleration of magnitude .30m/s squared during the time interval 2.0 sec. if the net force during the interval is .375N, what is the sailboats mass? what is the velocity of the boat after the 2.0s gust of wind?

Well, well, well, looks like our little sailboat is in a bit of a pickle! Let's dive into the ocean of physics and figure this out with a touch of humor, shall we?

To find the sailboat's mass, we can start by using Newton's second law, which states that force equals mass times acceleration (F = ma). In this case, the net force during the interval is given as 0.375 N, and the acceleration is 0.30 m/s²:

F = ma
0.375 N = m * 0.30 m/s²

Now, we can solve for m (the sailboat's mass):

m = 0.375 N / 0.30 m/s²

*drumroll please*

m = 1.25 kg

Ta-da! Our sailboat weighs in at 1.25 kg. Took a bit of math acrobatics, but we got there in the end! Now, let's set sail to figure out the velocity after the gust of wind.

The sailboat experiences a constant acceleration of magnitude 0.30 m/s² for the time interval of 2.0 seconds. So, to find the velocity, we can use the formula:

v = u + at

Here, u represents the initial velocity, a is the acceleration, and t is the time interval. The initial velocity is given as 0.33 m/s, and the acceleration is 0.30 m/s²:

v = 0.33 m/s + (0.3 m/s²) * 2.0 s

Calculations, ho!

v = 0.33 m/s + 0.6 m/s

v = 0.93 m/s

Ahoy there! After the gust of wind, the sailboat will be sailing at approximately 0.93 m/s. Hope that gives you a breezy answer to your question!

To find the sailboat's mass, we can use Newton's second law of motion:

F = ma

where:
F = net force (0.375 N)
m = mass of the sailboat (unknown)
a = acceleration of the sailboat (0.30 m/s^2; magnitude only, direction is not needed in this calculation)

Substituting the given values into the equation, we can solve for the mass:

0.375 N = m × 0.30 m/s^2

Dividing both sides of the equation by 0.30 m/s^2, we get:

m = 0.375 N / 0.30 m/s^2
m = 1.25 kg

Therefore, the mass of the sailboat is 1.25 kg.

To determine the velocity of the boat after the 2.0 s gust of wind, we need to calculate the change in velocity using the equation:

Δv = a × t

where:
Δv = change in velocity (unknown)
a = acceleration of the sailboat (0.30 m/s^2; magnitude only, direction is not needed in this calculation)
t = time interval (2.0 s)

Substituting the given values into the equation, we can find the change in velocity:

Δv = 0.30 m/s^2 × 2.0 s
Δv = 0.60 m/s

To find the final velocity, we need to consider the initial velocity of the sailboat. Since the sailboat is initially moving at 0.33 m/s west, the final velocity will be the vector sum of the initial velocity and the change in velocity caused by the gust of wind.

The vector sum can be calculated using the Pythagorean theorem:

vf^2 = vi^2 + Δv^2

where:
vf = final velocity (unknown)
vi = initial velocity (0.33 m/s)
Δv = change in velocity (0.60 m/s)

Substituting the given values into the equation and solving for vf:

vf^2 = (0.33 m/s)^2 + (0.60 m/s)^2
vf^2 = 0.1089 m^2/s^2 + 0.36 m^2/s^2
vf^2 = 0.4689 m^2/s^2

Taking the square root of both sides, we get:

vf = √(0.4689 m^2/s^2)
vf ≈ 0.685 m/s

Therefore, the velocity of the boat after the 2.0 s gust of wind is approximately 0.685 m/s.

To find the mass of the sailboat, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. Given that the net force acting on the sailboat is 0.375N and the acceleration is 0.30m/s², we can set up the following equation:

Net force = Mass * Acceleration

0.375N = Mass * 0.30m/s²

To solve for mass, we divide both sides of the equation by 0.30m/s²:

Mass = 0.375N / 0.30m/s²
Mass = 1.25 kg

Therefore, the mass of the sailboat is 1.25 kg.

To calculate the velocity of the boat after the 2.0s gust of wind, we need to use the equation of motion, which is:

Final velocity = Initial velocity + (Acceleration * Time)

The initial velocity is given as 0.33m/s, and the acceleration is given as 0.30m/s². We can plug in these values into the equation:

Final velocity = 0.33m/s + (0.30m/s² * 2.0s)
Final velocity = 0.33m/s + 0.60m/s
Final velocity = 0.93m/s

Therefore, the velocity of the sailboat after the 2.0s gust of wind is 0.93m/s.