Question

In her Physics lab, Krystal rolls a 2g marble down a ramp and off the table with a horizontal velocity of 1.6m/s. The marble falls perfectly (naturally) in a cup placed 0.60m from the table's edge. How high is the table?

Answer 1

To determine the height of the table, the time the marble was in the air was calculated based on its horizontal velocity and distance traveled. Then, the vertical distance was found using the time and acceleration due to gravity, revealing the table to be approximately 0.6893 meters tall.

Step-by-step explanation:

The question concerns a Physics experiment where Krystal rolls a marble off a table. To find how high the table is, we need to use the given horizontal velocity and the distance the marble traveled horizontally to figure out the time the marble was in the air. The formula we'll use is:

• Horizontal distance = Horizontal velocity * Time

Given that the horizontal velocity (vx) is 1.6 m/s, and the horizontal distance (d) is 0.60 m, we can solve for the time (t).

d = vx * t
t = d / vx = 0.60 m / 1.6 m/s = 0.375 s

Now, we know that the marble is in the air for 0.375 seconds. During this time, it's also moving vertically under the influence of gravity. This vertical motion is unrelated to the horizontal motion and can be analyzed separately using the equation:

• Vertical distance = 1/2 * g * t2

Where g is the acceleration due to gravity (9.81 m/s2). Now we can calculate the height (h) of the table from which the marble fell:

h = 1/2 * g * t2
h = 1/2 * 9.81 m/s2 * (0.375 s)2 = 0.6893 m

The table is approximately 0.6893 meters tall.