For how long is she in contact with the trampoline?
To determine the total time of contact, we add the upward and downward times: 0.44 s + 0.16 s = 0.60 s. Therefore, the student is in contact with the trampoline for approximately 0.60 seconds.
Calculating Time of Contact
The student bouncing on the trampoline experiences both upward and downward motions. To find the total time of contact, we need to consider each phase separately.
Upward Motion:
First, let's calculate the time the student spends moving upward. At her highest point, her feet are 95 cm above the trampoline. We can use the equation h = (1/2) * g * t^2, where h is the displacement, g is the acceleration due to gravity, and t is the time. By rearranging the equation, we find t = √(2h / g). Substituting the values, we get t = √(2 * 0.95 m / 9.8 m/s^2) ≈ 0.44 s.
Downward Motion:
Next, we calculate the time the student spends moving downward. The trampoline sags 25 cm before propelling her back up, which is the displacement from the highest point to the rest position. Using the same equation, t = √(2h / g), we find t = √(2 * 0.25 m / 9.8 m/s^2) ≈ 0.16 s.
Total Time of Contact:
By adding the upward and downward times, we get 0.44 s + 0.16 s = 0.60 s. Therefore, the student is in contact with the trampoline for approximately 0.60 seconds.