Answer:
To find the height at which the two objects will first meet, we need to use the equations of motion for free fall and vertical upward motion.
The equation for free fall is:
h = h0 + v0t + (1/2)at^2
where h is the height of the object at time t, h0 is the initial height, v0 is the initial velocity (which is zero for free fall), and a is the acceleration due to gravity (which is 9.8 m/s^2 downward).
The equation for vertical upward motion is:
h = h0 + v0t - (1/2)gt^2
where h is the height of the object at time t, h0 is the initial height, v0 is the initial velocity, and g is the acceleration due to gravity (which is 9.8 m/s^2 downward).
We know that the first object is in free fall, and that it began at a height of 22.0 m. We also know that the second object was launched upward with an initial velocity of 32.0 m/s, 1.10 s after the first object was released.
We can use these values to find the height of the first object at the time the second object is launched:
h1 = 22.0 + 0 + (1/2)(-9.8)(1.10^2) = 20.27 m
We can use this value as the initial height for the second object:
h2 = 20.27 + 32.0(1.10) - (1/2)(-9.8)(1.10^2) = 37.47 m
Now we need to find the time at which the two objects will meet. We can use the height of the first object at the time the second object is launched, and the equation for free fall to find the time it takes for the first object to reach the height of the second object:
37.47 = 20.27 + 0 + (1/2)(-9.8)t^2
Solving for t, we find that the objects will meet at a time of approximately 1.47 seconds.
Finally, we can use this time to find the height at which they will meet:
h = 22.0 + 0 + (1/2)(-9.8)(1.47^2) = 37.47 m
So the objects will first meet at a height of 37.47 m above the ground.