Answer: The two balls will collide at a height of 7.16 meters above the ground.
Step-by-step explanation:
Assuming no air resistance, the two balls will collide when they are at the same height and their paths intersect.
The time it takes for the first ball to fall to the ground can be calculated using the formula:
h = (1/2)gt^2
where h is the initial height (10 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes to fall.
Plugging in the values, we get:
10 = (1/2)(9.8)t^2
Solving for t, we get:
t = sqrt(2*10/9.8) = 1.43 seconds
During this time, the second ball will be traveling upwards. The height it reaches can be calculated using the formula:
h = v0t + (1/2)at^2
where v0 is the initial velocity (10 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time it takes to reach maximum height.
Plugging in the values, we get:
h = 10(1.43) + (1/2)(-9.8)(1.43)^2 = 7.16 meters
Therefore, the two balls will collide at a height of 7.16 meters above the ground.