You are thinking about taking gymnastics, so you go to the facility and get an idea of what to expect by looking out from the viewing room. The viewing room window is 4.30 m above the trampoline directly below, so it is perfect for viewing the the facility. Occasionally someone jumps past the window and then back down. On one occurrence a gymnast went up past the window and came back down; as he passed the window on the way down, you notice that his speed is 14.1 m/s.
V^2 = Vo^2 + 2g*h = 14.1^2 + 19.6*4.3 =
V = ?
To determine the height the gymnast reaches above the window, we can use the concept of conservation of mechanical energy. The mechanical energy of the gymnast can be expressed as the sum of his potential energy (PE) and kinetic energy (KE).
Initially, when the gymnast reaches the highest point above the window, his kinetic energy is zero (since he momentarily stops at the top of his jump). Therefore, all the energy is in the form of potential energy.
The potential energy is given by the equation:
PE = m * g * h
where m is the mass of the gymnast, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height reached above the window.
When the gymnast returns to the window, all the potential energy is converted into kinetic energy since his speed is given.
KE = (1/2) * m * v^2
where v is the speed of the gymnast (14.1 m/s).
According to the conservation of mechanical energy, the potential energy at the highest point is equal to the kinetic energy when the gymnast passes the window:
m * g * h = (1/2) * m * v^2
By rearranging the equation, we can solve for the height h:
h = (1/2) * v^2 / g
Now, let's substitute the given values into the equation:
h = (1/2) * (14.1 m/s)^2 / 9.8 m/s^2 = 10.152 m
Therefore, the height reached above the window by the gymnast is approximately 10.152 meters.