Final answer:
Unfortunately, without specific values for time, radius, and angular velocity, it is not possible to determine the approximations for the angular speed of the skater during the leap, the centripetal acceleration of the skater's hand, or the speed of the skater's hand.
Step-by-step explanation:
7.25: Angular speed is defined as the change in angle per unit of time. In this case, the skater is completing a leap. Since we know the time it takes for the skater to complete the leap is unknown, we cannot calculate the exact angular speed. Therefore, we cannot determine the approximate angular speed of the skater during the leap.
7.26: When the skater's arms are fully extended during the jump, the centripetal acceleration of the skater's hand can be calculated using the formula a = rω², where a is the centripetal acceleration, r is the radius (distance from the axis of rotation to the skater's hand), and ω is the angular velocity. Without the values for r and ω, it is not possible to calculate the approximate centripetal acceleration.
7.27: The speed of the skater's hand can be calculated using the formula v = rω, where v is the speed, r is the radius (distance from the axis of rotation to the skater's hand), and ω is the angular velocity. Without the values for r and ω, it is not possible to calculate the approximate speed of the skater's hand.