Final answer:
To find the vertical component of acceleration for the module at time tm = t0 - σ = 325s, you need to calculate the final vertical velocity and the time it takes for the module to reach the final position. Then, you can use the formula a = (vy - voy) / t to find the vertical component of acceleration.
Step-by-step explanation:
The vertical component of acceleration for the module at time tm = t0 - σ = 325s can be determined by finding the change in vertical velocity over time. The initial vertical velocity, voy, is found using the formula voy = vo sinθ, where vo is the initial velocity and θ is the angle of the trajectory. Substituting the given values, voy = (25.0 m/s) * sin(35.0°) = 14.3 m/s. The final vertical velocity, vy, can be found using the formula vy = voy + at, where vy is the final vertical velocity, a is the vertical acceleration, and t is the time. Since the vertical position changes from y = 0 to y = -20.0 m, we can use the equation y = voyt + 0.5at² to find the time it takes for the module to reach the final position. Substituting the known values, -20.0 m = (14.3 m/s)t - 0.5(9.8 m/s²)t². Solving this quadratic equation will give us the time it takes for the module to reach the final position. Once we have this time, we can substitute it into the equation vy = voy + at to find the final vertical velocity. Finally, the vertical component of acceleration, a, can be found using the formula a = (vy - voy) / t.