To determine how far apart Ball 1 and Ball 2 are after 5.02 seconds, we need to calculate the distance each ball has traveled during that time.
1. Calculate the distance Ball 1 has traveled after 5.02 seconds:
Since Ball 1 was dropped and not thrown, it experiences free fall with an acceleration of approximately 9.8 m/s^2 downwards. We can use the equation for distance traveled during free fall:
d1 = (1/2) * g * t1^2, where d1 is the distance traveled by Ball 1, g is the acceleration due to gravity, and t1 is the time Ball 1 has been falling.
Plugging in the values:
d1 = (1/2) * 9.8 m/s^2 * (5.02 s)^2
d1 = 122.98 m (rounded to two decimal places)
2. Calculate the distance Ball 2 has traveled after 5.02 seconds:
Since Ball 2 was thrown downward, its motion can be modeled using the equation:
d2 = v2 * t2, where d2 is the distance traveled by Ball 2, v2 is the velocity of Ball 2, and t2 is the time Ball 2 has been traveling.
Plugging in the values:
d2 = 3.49 m/s * (5.02 s - 3.14 s)
d2 = 6.71 m (rounded to two decimal places)
3. Determine the distance between Ball 1 and Ball 2 after 5.02 seconds:
To find the distance between the balls, we subtract the distance traveled by Ball 2 from the distance traveled by Ball 1:
Distance = d1 - d2
Distance = 122.98 m - 6.71 m
Distance = 116.27 m (rounded to two decimal places)
Therefore, after 5.02 seconds from when Ball 1 was released, Ball 1 and Ball 2 will be approximately 116.27 meters apart.