a person pushes on a hockey puck with their stick at an angle so the vertical force is 22N down and the horizontal force is 45N forward. Assume the ice is frictionless.

What is the actual force the hockey player transmits to the puck?
what is the work done by the person pushing the hockey stick if they push the puck for 3 seconds as it moves with a constant velocity of 22m/s forward?

Please help I don't know how to start this question

Oh, hey there! Don't worry, I'm here to help you out with that question. Now, let's get the puck rolling!

To find the actual force transmitted by the hockey player to the puck, we can use the Pythagorean theorem because the forces are acting at right angles to each other. So, let's calculate it together:

Vertical force (down) = 22N
Horizontal force (forward) = 45N

Let's call the actual force F. According to Pythagoras:

F² = (Vertical force)² + (Horizontal force)²

F² = 22N² + 45N²

F² = 484N² + 2025N²

F² = 2509N²

Taking the square root of both sides, we get:

F ≈ 50.09N

So, the actual force the hockey player transmits to the puck is approximately 50.09N.

Now, moving on to the work done by the person pushing the hockey stick. Since the puck is moving with a constant velocity, we can assume there is no acceleration, and thus, no net work is being done on the puck. Therefore, the work done by the person pushing the puck is zero (0 J).

Keep in mind that this is a simplified scenario without any friction, but it should get you started. And remember, never ask a hockey puck for advice—they're always "slippery" when it comes to giving answers!

To find the actual force the hockey player transmits to the puck, we can use vector addition. Since the vertical force is 22N down and the horizontal force is 45N forward, we can use Pythagoras' theorem to find the resultant force.

The resultant force (F) can be found using the equation:

F = √(F_horizontal^2 + F_vertical^2)

Substituting the values:

F = √(45^2 + 22^2)
F = √(2025 + 484)
F = √2509
F ≈ 50.09N

Therefore, the actual force the hockey player transmits to the puck is approximately 50.09N.

To find the work done by the person pushing the hockey stick, we can use the equation:

Work (W) = Force (F) × Distance (d) × Cosine of the angle between the force and the direction of motion (θ)

In this case, the puck is moving with a constant velocity of 22m/s forward. Since work is defined as the product of force and displacement, the distance travelled by the puck during the 3-second time interval is given by:

Distance (d) = Velocity (v) × Time (t)
d = 22m/s × 3s
d = 66m

The angle (θ) between the force and the direction of motion is 0 degrees, as the force and the motion are in the same direction.

Substituting the values, we get:

W = F × d × cos(θ)
W = 50.09N × 66m × cos(0)
W = 50.09N × 66m × 1
W = 3303.6 Joules

Therefore, the work done by the person pushing the hockey stick is 3303.6 Joules.

To find the actual force transmitted to the hockey puck, you can use vector addition to find the resultant force.

The vertical force of 22 N acting downward and the horizontal force of 45 N acting forward form a right-angled triangle. To find the resultant force, you can use the Pythagorean theorem, which states that the square of the hypotenuse (the resultant force in this case) is equal to the sum of the squares of the other two sides. In this case, the vertical and horizontal forces represent the sides of the triangle, and the resultant force (actual force transmitted to the puck) represents the hypotenuse.

Let's calculate it step by step:

Step 1: Calculate the magnitude of the resultant force
Using the Pythagorean theorem:
Resultant force = √(vertical force^2 + horizontal force^2)
Resultant force = √(22^2 + 45^2)
Resultant force = √(484 + 2025)
Resultant force = √2509
Resultant force ≈ 50.09 N (rounded to two decimal places)

Step 2: Determine the direction of the resultant force
To find the direction of the force, you can use trigonometry.

The angle can be found using the inverse tangent (arctan) function:
Angle = arctan(vertical force / horizontal force)
Angle = arctan(22 / 45)
Angle ≈ 27.565 degrees (rounded to three decimal places)

Therefore, the actual force transmitted to the hockey puck is approximately 50.09 N at an angle of 27.565 degrees with the horizontal.

For the second part of your question, to find the work done by the person pushing the hockey stick, you can use the equation:

Work = Force × Distance × cosθ

Here, the force is the actual force transmitted to the puck (50.09 N), the distance is the displacement of the puck (which is equal to velocity × time = 22 m/s × 3 seconds = 66 m), and θ is the angle between the force and the displacement (which is the same as the angle found in the first part, 27.565 degrees).

Step 1: Convert the angle to radians
Angle (in radians) = Angle (in degrees) × (π / 180)
Angle (in radians) ≈ 27.565 × (π / 180) ≈ 0.481 radians (rounded to three decimal places)

Step 2: Calculate the work done
Work = 50.09 N × 66 m × cos(0.481)
Work ≈ 3314.33 J (rounded to two decimal places)

Therefore, if the person pushes the puck for 3 seconds as it moves with a constant velocity of 22 m/s forward, they will do approximately 3314.33 Joules of work.

a. X = 45 N.

Y = -22 N.

F^2 = 45^2 + (-22)^2 = 2,509
F = 50.09 N.

b. d = 22m/s * 3s = 66 m.

Work = F*d = 50.09 * 66 = 3306 Joules.