Amy age 8 27kg 127cm
Bruce age 12 41kg 149cm
Both Amy and Bruce are learning gymnastics and having trouble being able to get enough height and time in the air to do a back somersault without the coach spotting them.
The coach gives them homework to just focus on jumping straight up and landing back down. He tells them from a standing position with arms 90 degrees in front of them to bring hands down past their hips as far as they can while squatting until their knees are at a 90 angle and the as they stand up from the squat to bring their hands forward and leap straight into the air trying to touch the ceiling!
1. Calculate the momentum for both Amy and Bruce created by the kinetic and elastic energy of the counter movements before the leap.
2. Calculate Accelleration and apply to F=ma to get the Ground Reaction force
3. If each of them precisely gets to a 90 degree knee flex during squat, and rotate their arms from 90 degrees to 270 degrees then back up to 0 degrees, so their arms are at 270 degrees when knees at 90 degrees and arms return to 90 degrees at point their knees return to 0 degrees, what is the height each can reach and the time in the air before they land.
Assume their height is 1/2 above waist and 1/2 below and their knees are 1/2 of the distance between waist and ground.
To calculate the answers to the given questions, we need to know some physical properties of Amy and Bruce, such as their mass and height. Based on the information provided, Amy's mass is 27 kg, and her height is 127 cm. Bruce's mass is 41 kg, and his height is 149 cm. Now let's go step by step to find the solutions.
1. Calculate the momentum for both Amy and Bruce created by the kinetic and elastic energy of the counter movements before the leap:
Momentum (p) is calculated by the equation p = mv, where m is mass and v is velocity.
For Amy:
Mass (m) = 27 kg
Velocity (v) = change in speed during the counter movement
For Bruce:
Mass (m) = 41 kg
Velocity (v) = change in speed during the counter movement
To calculate the velocities, we need more information about the counter movements, such as the speed and duration. Without these details, we cannot provide a specific numerical answer.
2. Calculate Acceleration and apply to F=ma to get the Ground Reaction force:
To calculate acceleration (a), we need to know the change in velocity and the time taken to achieve that change. Without this information, it is not possible to calculate acceleration accurately or determine the ground reaction force (F).
3. Calculate the height each can reach and the time in the air before they land:
To calculate the height and time in the air, we can use the equations of motion. Given that Amy and Bruce start from a squat position and jump vertically, we can assume zero initial velocity in the vertical direction (u = 0) and the acceleration due to gravity (-9.8 m/s^2).
The kinematic equation to calculate the height (h) reached is:
h = (v^2 - u^2) / (2g)
The kinematic equation to calculate the time (t) in the air is:
t = (v - u) / g
For both equations, v is the final vertical velocity, u is the initial vertical velocity, and g is the acceleration due to gravity.
To calculate the height and time in the air, we need to know the final vertical velocities for Amy and Bruce at the highest point of their jumps. Without this information, we cannot provide specific numerical answers.
In conclusion, the specific calculations to find the momentum, acceleration, ground reaction force, height, and time in the air require additional information about the counter movements and the final velocities.