(a) Suppose a hockey puck slides down a frictionless ramp with an acceleration of 5.60 m/s2. What angle does the ramp make with respect to the horizontal?

To determine the angle of the ramp with respect to the horizontal, we need to use trigonometry. The acceleration of an object sliding down an inclined plane is related to the angle of the plane and the acceleration due to gravity.

We can start by using the formula for acceleration on an inclined plane:

a = g*sin(θ)

Where "a" is the acceleration of the puck (5.60 m/s²), "g" is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the ramp.

Rearranging the equation, we can solve for θ:

sin(θ) = a / g

sin(θ) = 5.60 m/s² / 9.8 m/s²

By plugging these values into a calculator, we can find the value of sin(θ). Then, to find θ itself, we can use the inverse sine function (sin⁻¹) or arcsine:

θ = sin⁻¹(a / g)

θ = sin⁻¹(5.60 m/s² / 9.8 m/s²)

Calculating this expression using a calculator will give you the angle θ.

To find the angle of the ramp with respect to the horizontal, we can use the formula for the acceleration of an object sliding down a ramp:

a = g * sinθ

where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the ramp with respect to the horizontal.

Rearranging the formula, we get:

sinθ = a / g

Plugging in the given values, we have:

sinθ = 5.60 m/s^2 / 9.8 m/s^2

sinθ ≈ 0.571

To find the angle θ, we need to take the inverse sine (arcsin) of both sides:

θ ≈ arcsin(0.571)

Calculating this, we find:

θ ≈ 34.82°

Therefore, the angle that the ramp makes with respect to the horizontal is approximately 34.82°.