A person is jogging at 3.5 m/s and grabs a rope that is hanging vertically from a tree. How high can the student swing?
He can swing upwards a vertical distance H, such that
M*g*H = M*V^2/2
H = V^2/(2g)
H = 1.25 meters
To determine the maximum height the person can swing, we can use the concept of conservation of mechanical energy. The initial kinetic energy of the person when they grab the rope will be converted into potential energy as they swing upward. At the highest point of the swing, all the initial kinetic energy will have been converted into potential energy.
To calculate the maximum height, we need to find the initial kinetic energy of the person. The kinetic energy (KE) formula is given by:
KE = 1/2 * mass * velocity^2
Since the mass of the student is not given, we can assume a standard value of 70 kg for an average person. We are given the velocity as 3.5 m/s.
Plugging in these values, we can calculate the initial kinetic energy (KE):
KE = 1/2 * 70 kg * (3.5 m/s)^2
KE = 1/2 * 70 kg * 12.25 m^2/s^2
KE = 1/2 * 70 kg * 12.25 J
KE = 429.25 J
Now, we know that the potential energy (PE) at the highest point is equivalent to the initial kinetic energy (KE). The potential energy formula is given by:
PE = mass * gravitational acceleration * height
The mass and gravitational acceleration remain constant, so we can set the initial kinetic energy equal to the potential energy at the highest point:
429.25 J = mass * 9.8 m/s^2 * height
Since we assumed the mass is 70 kg, we can calculate the height (h):
429.25 J = 70 kg * 9.8 m/s^2 * h
h = 429.25 J / (70 kg * 9.8 m/s^2)
h ≈ 0.62 m
Therefore, the person can swing to a maximum height of approximately 0.62 meters.