a ball rolls off the edge of a table with a velocity of 1m/s if the table is 1m talla, how far from the edge of the table does the ball strike the floor?, how long does the ball fell?
a ball rolls off the edge of a table with a velocity of 1m/s if the table is 1m talla, how far from the edge of the table does the ball strike the floor?, how long does the ball fell?
falls 1 meter with zero initial speed down
h = 1 +0 t - 4.9 t^2
4.9 t^2 = 1 when h = 0 (floor level)
t = 0.452 seconds to reach the floor
so
d = u t = 1 m/s * 0.452 s = 0.453 meter horizontal
now I suspect you are finished, but the distance from the edge of the table is actually 1 meter down and 0.452 meter horizontal
so really
distance = sqrt (.452^2 + 1^2)
To find out how far from the edge of the table the ball strikes the floor, you can use the equation of motion for an object falling freely under gravity:
h = (1/2) * g * t^2
where:
h = height of the table (1m),
g = acceleration due to gravity (approximately 9.8 m/s^2),
t = time of fall.
Since the initial velocity of the ball rolling off the table is horizontal, it does not affect the vertical motion of the ball. Therefore, there is no need to consider the initial velocity in this scenario.
First, let's find the time it takes for the ball to hit the floor. Rearranging the equation, we have:
t^2 = (2h) / g
Substituting the values, we get:
t^2 = (2 * 1) / 9.8
t^2 = 0.2041
t ≈ √(0.2041)
t ≈ 0.452 s (rounded to 3 decimal places)
Now that we know the time of fall, we can determine the horizontal distance covered by the ball using the equation:
d = v * t
where:
d = horizontal distance,
v = horizontal velocity (1 m/s),
t = time of fall (0.452 s).
Substituting the values, we get:
d = 1 * 0.452
d ≈ 0.452 m (rounded to 3 decimal places)
Therefore, the ball strikes the floor approximately 0.452 meters from the edge of the table.
To summarize:
- The ball strikes the floor approximately 0.452 meters from the edge of the table.
- The ball falls for approximately 0.452 seconds.