a marble that is rolling across a lab table has a velocity of 0.7m/s. If the table is 0.9m high, how far from the edge of the table will the ball travel in the horizontel direction before it hits the floor ?
To determine how far the marble will travel in the horizontal direction before hitting the floor, we need to find the time it takes for the marble to fall from the edge of the table to the floor.
We can start by calculating the time it takes for the marble to fall from a height of 0.9 m. The formula to calculate the time for an object to fall freely under gravity is given by:
t = √(2h / g)
Where:
t = time taken to fall
h = height
g = acceleration due to gravity (approximately 9.8 m/s²)
Plugging in the given values, we have:
t = √(2 * 0.9 m / 9.8 m/s²)
t = √(0.1837)
t ≈ 0.428 s
So, it takes approximately 0.428 seconds for the marble to fall from the edge of the table to the floor.
Now, we can calculate the horizontal distance the marble will travel in that time. Since the marble has a horizontal velocity of 0.7 m/s and the formula for distance is given by:
d = v * t
Where:
d = distance
v = velocity
t = time
Plugging in the values, we have:
d = 0.7 m/s * 0.428 s
d ≈ 0.3 m
Therefore, the marble will travel approximately 0.3 meters horizontally before it hits the floor.