Final answer:
By using the equations of motion for each stone and setting their displacements equal, we can solve for the time at which they are at the same height. Subsequently, the height can be found by substituting back into one of the displacement equations. The downward speed of the first stone as they pass each other is calculated using the final velocity equation.
Step-by-step explanation:
To determine when two stones thrown vertically upward will be at the same height, we can use the equations of motion under uniform acceleration due to gravity. The equation s = ut + (1/2)at² is used, where s is the displacement, u is the initial speed, t is time, and a is acceleration due to gravity. Since acceleration due to gravity is downward, we take it as negative (usually -9.81 m/s²).
The first stone is thrown at t = 0, so for the first stone (stone 1):
s1 = 22.10 m/s × t - (1/2)× 9.81 m/s² × t²
The second stone (stone 2) is thrown 1.760 seconds later, so for stone 2:
s2 = 22.10 m/s × (t - 1.760 s) - (1/2)× 9.81 m/s² × (t - 1.760 s)²
At the same height, s1 = s2. By equating the above two equations and solving for t, we can find the time when they are at the same height.
To find the height when they pass each other, we substitute this time value back into one of the original displacement equations. To find the downward speed of the first stone when they pass each other, we use the formula v = u + at, where v is the velocity at that time. Keep in mind the signs of u and a when doing these calculations.