Question

a marble rolls horizontally at 10 m/s off of a table and lands on the floor 5.5 m away. Determine the time it took the marble to fall from the table and hit the ground. From what height did the marble fall?

Answer 1

The marble was in the air for 0.55 seconds before it hit the ground, and it fell from a height of 1.48 meters.

Step-by-step explanation:

Time of Flight and Height of the Fall

To determine the time it took the marble to fall from the table and hit the ground, we can use the horizontal motion of the marble. Since the horizontal velocity of the marble is constant (10 m/s) and it lands 5.5 m away from the edge of the table, we can calculate the time it was in the air (time of flight) using the formula:

distance = speed × time

Rearranging the formula for time gives us:

time = distance / speed

Substituting in the known values:

time = 5.5 m / 10 m/s = 0.55 seconds

This means the marble was in the air for 0.55 seconds.

To find the height (h) from which the marble fell, we use the formula for the vertical distance covered by an object in free fall under the influence of gravity (g = 9.8 m/s²):
h = 0.5 × g × time²

Substituting in the time:

h = 0.5 × 9.8 m/s² × (0.55 s)²

h = 0.5 × 9.8 m/s² × 0.3025 s²

h = 1.48 m

The marble fell from a height of 1.48 meters.