I need help with this question...A skateboarder, starting from rest, rolls down a 12.0-m ramp. When she arrives at the bottom of the ramp her speed is 8.90 m/s. (a) Determine the magnitude of her acceleration, assumed to be constanIf the ramp is inclined at 21.5° with respect to the ground, what is the component of her acceleration that is parallel to the ground?

9a) Vfinal = sqrt(2aS) where S is the distance travelled.

Solve that for a, the acceleration down the ramp.

(b) a cos 21.5 is the acceleration component parallel to the ground.

To determine the magnitude of the skateboarder's acceleration, we can use the kinematic equation:

v^2 = u^2 + 2as

Where:
v = final velocity = 8.90 m/s
u = initial velocity = 0 m/s (starting from rest)
a = acceleration
s = distance traveled = 12.0 m

Rearranging the equation, we have:

a = (v^2 - u^2) / (2s)

Substituting the given values, we get:

a = (8.90^2 - 0^2) / (2 * 12.0)
a = 79.21 / 24.0
a = 3.3 m/s^2

Therefore, the magnitude of the skateboarder's acceleration is 3.3 m/s^2.

To find the component of her acceleration parallel to the ground, we can use trigonometry. Since the ramp is inclined at 21.5° with respect to the ground, the component of acceleration parallel to the ground can be calculated using:

acceleration_parallel = acceleration * cosθ

Where θ is the angle of incline.

Substituting the values, we have:

acceleration_parallel = 3.3 m/s^2 * cos(21.5°)
acceleration_parallel = 3.3 m/s^2 * 0.928
acceleration_parallel ≈ 3.06 m/s^2

Therefore, the component of her acceleration that is parallel to the ground is approximately 3.06 m/s^2.

To find the magnitude of the skateboarder's acceleration, we can use the physics equation for constant acceleration:

v^2 = u^2 + 2as

where:
- v is the final velocity (8.90 m/s)
- u is the initial velocity (0 m/s, as she starts from rest)
- a is the acceleration
- s is the displacement (12.0 m)

Rearranging the equation to solve for acceleration:

a = (v^2 - u^2) / (2s)

Plugging in the given values:

a = (8.90^2 - 0^2) / (2 * 12.0)

Now, let's calculate the result to find the magnitude of her acceleration:

a = (79.21 - 0) / 24 = 3.3 m/s^2

So, the magnitude of her acceleration is 3.3 m/s^2.

To find the component of her acceleration parallel to the ground, we need to consider the angle of the ramp. The acceleration can be divided into two components: one parallel to the ramp and one perpendicular to the ramp.

The component of acceleration parallel to the ground is calculated using the equation:

a_parallel = a * sin(theta)

where:
- a_parallel is the component of acceleration parallel to the ground
- a is the magnitude of acceleration
- theta is the angle of the ramp with respect to the ground (21.5°)

Plugging in the values:

a_parallel = 3.3 * sin(21.5°)

Using a calculator, we can find the result:

a_parallel = 1.2 m/s^2

Therefore, the component of her acceleration parallel to the ground is 1.2 m/s^2.

Her component