What is the acceleration of a skateboard down a ramp inclined at 19.5 degrees to the horizontal?

3.271 is the answer.

This shouldn't be too tough, but I can't get it. Thanks!

Okay, I see that it's g sin 19.5 degrees, but why isn't it g divided by sin 19.5?

To find the acceleration of the skateboard down the ramp, you can use Newton's second law of motion and resolve the forces acting on the skateboard along the ramp. Here's how you can do it:

1. Draw a free-body diagram: Start by drawing a diagram representing the skateboard on the inclined ramp. Label the forces acting on the skateboard, such as the gravitational force (mg) acting straight down and the normal force (N) perpendicular to the ramp.

2. Resolve the forces: Break down the gravitational force into two components: one parallel to the ramp (mg*sinθ) and one perpendicular to the ramp (mg*cosθ). Here, θ represents the angle of incline of the ramp, which is given as 19.5 degrees in this case.

3. Find the net force: Since the skateboard is moving down the ramp, the net force acting on it in the direction of motion is the force parallel to the ramp (mg*sinθ). Recall that F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.

4. Substitute the values: Plug in the known values into the equation. The mass of the skateboard is not provided in the question, so you will need to know it to find the acceleration. Once you have the mass, substitute it, along with the value of g (acceleration due to gravity) and the angle θ, into the equation.

For example, if the mass of the skateboard is 10 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, you can calculate the net force:

Net force = (10 kg) * (9.8 m/s^2) * sin(19.5 degrees) ≈ 33.042 N

5. Calculate the acceleration: Now that you have the net force, divide it by the mass of the skateboard to find the acceleration:

Acceleration = Net force / Mass

For example, if the net force is 33.042 N and the mass is 10 kg:

Acceleration = 33.042 N / 10 kg ≈ 3.3042 m/s^2

Therefore, the approximate acceleration of the skateboard down the ramp is 3.3042 m/s^2. Note that this value has been rounded to four decimal places.