Final answer:
The angle of a frictionless ramp causing a 4.90 m/s² acceleration is 30°. The hockey puck takes approximately 1.63 seconds to reach the bottom of a 6.50 m ramp. Doubling the puck's mass does not change its acceleration down the ramp.
Step-by-step explanation:
Understanding the Motion of a Hockey Puck on a Ramp
When a hockey puck slides down a frictionless ramp, its acceleration is related to the angle of the ramp and the force of gravity. To find the angle, θ, we can use the equation for acceleration on an inclined plane: a = g ⋅ sin(θ), where a is the acceleration and g is the acceleration due to gravity.
a) Reorganizing the above equation gives sin(θ) = a/g. Plugging in the values, we get sin(θ) = 4.90 m/s² / 9.81 m/s², which results in θ = sin⁻¹(4.90/9.81). The angle of the ramp is approximately 30°.
b) To find how long it takes the puck to reach the bottom of the 6.50 m ramp, we can use the kinematic equation: s = ½ at². Solving for t, we get t = √(2s/a), which results in t = √(2·6.50 m / 4.90 m/s²). The time taken is approximately 1.63 seconds.
c) If the mass of the puck is doubled, it will not affect the acceleration down the ramp because acceleration due to gravity is mass-independent. Thus, the new acceleration of the puck remains 4.90 m/s².