A puck slides across a smooth, level tabletop at height H at a constant speed v_o. It slides off the edge of the table and hits the floor a distance x away as shown in the figure. What is the relationship between the distances x and H?

Question

Quizplus · Accepted Answer

The horizontal motion of the puck is not affected by its height above the table, so it will continue to move at a constant speed v_o once it leaves the table. The only force acting on it after leaving the table is gravity, which will cause the puck to accelerate downward at a rate of g. Using the equation of motion for vertical motion, we can find the time it takes for the puck to hit the ground: H = (1/2)gt^2 t = sqrt(2H/g) Once we know the time, we can use the horizontal speed and the time to find the distance x that the puck travels before hitting the ground: x = v_o * t Substituting the expression for t: x = v_o * sqrt(2H/g) We can see that x is proportional to sqrt(H), so the correct relationship between x and H is: x ∝ sqrt(H) or x = k * sqrt(H) where k is some constant. This means that x will increase as the square root of H increases. Therefore, the answer is choice A.

A Puck Slides Across a Smooth, Level Tabletop at Height