Question

A physics student playing with an air hockey table (a frictionless surface) finds that if she gives the puck a velocity of 3.78 m/s along the length ( 1.79 m ) of the table (the x-direction) at one end, by the time it has reached the other end the puck has drifted a distance 2.55 cm to the right (the y-direction). The puck still has a x-component of its velocity of 3.78 m/s when it reaches the other end of the table.

She concludes correctly that the table is not level and calculates its inclination (tilt) from the above information.

What is the angle of inclination?

Answer 1

consider the motion along the X-direction :

v_ox = velocity along x-direction = 3.78 m/s

x = distance travelled = 1.79 m

t = time of travel = ?

using the equation

x =  v_ox t

1.79 = (3.78) t

t = 0.474 sec

consider the motion along the y-direction

v_oy = initial velocity along the y-direction = 0 m/s

a = acceleration = g Sin

y = displacement = 2.55 cm = 0.0255 m

t = time = 0.474 sec

Using the equation

y = v_oy t + (0.5) a t²

0.0255 = 0 (0.474) + (0.5) (9.8 Sin) (0.474)²

Sin = 0.0232

= 1.33 deg