A physics student playing with an air hockey table (a frictionless surface) finds that if she gives the puck a velocity of 5.30 m/s along the length (2.80 m) of the table at one end, by the time it has reached the other end the puck has drifted 5.19 cm to the right but still has a velocity component along the length of 5.30 m/s. She correctly concludes that the table is not level and correctly calculates its inclination from the above information. What is the angle of inclination?
To find the angle of inclination of the table, we can first determine the change in elevation from one end of the table to the other.
Given:
- Initial velocity along the length (v₀) = 5.30 m/s
- Distance along the length of the table (d) = 2.80 m
- Displacement perpendicular to the length (d⊥) = 5.19 cm = 0.0519 m
Since the table is frictionless, only gravity can cause the puck to drift to the right.
Using the equation of motion for uniformly accelerated linear motion, we have:
d⊥ = (1/2) * a * t²
Here, a represents the acceleration due to gravity and t represents the time it takes for the puck to reach the other end of the table.
To find t, we can use the equation of motion: d = v₀ * t + (1/2) * a * t²
Rearranging the equation, we get:
t = (d - (1/2) * a * t²) / v₀
Since the initial velocity at the other end of the table is also 5.30 m/s, we have:
d = v₀ * t
Substituting this equation into the previous equation, we have:
t = (v₀ * t - (1/2) * a * t²) / v₀
Simplifying the equation gives:
t = t - (1/2) * a * t / v₀
Solving for t, we find:
(1/2) * a * t / v₀ = 0
Since t ≠ 0, we have:
a = 0
This means that the acceleration due to gravity is zero, which is not possible. Therefore, there is an error in the problem statement, or the description of the situation is not consistent with the laws of physics. Please check the information provided or clarify any additional details.