a high jumper approaches the takeoff point at a speed of 7.20 m/s. Assuming that only this speed determines the height to which he can rise, find the maximum height at which the jumper can clear the bar.
im sorry but i cant tell you the answer ill be gladly to check though
KE runner=PE change of runner
1/2 m v^2=mgh solve for h.
This is a bit misleading, the runners center of gravity starts near his waist, about 1.2 meters above the ground. So, I would add that to h. Your teacher probably wouldn't
so would the m's cancel out and leave 1/2 v^2= gh
1/2 (7.20)^2=9.8h
25.92=9.8h
h=2.64
To find the maximum height at which the jumper can clear the bar, we can use the principle of conservation of mechanical energy. The mechanical energy at the takeoff point must be equal to the mechanical energy at the maximum height reached by the jumper.
First, let's find the kinetic energy of the jumper at the takeoff point. The formula for kinetic energy is:
Kinetic Energy = 0.5 * mass * velocity^2
Assuming the mass of the jumper is 1 kg, the kinetic energy is:
Kinetic Energy = 0.5 * 1 kg * (7.20 m/s)^2 = 25.92 Joules
At the maximum height, all of the kinetic energy is converted into potential energy. So, the potential energy at the maximum height can be calculated:
Potential Energy = mass * gravitational acceleration * height
The formula for potential energy is derived from Newton's second law, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by the acceleration (a) of the object. In this case, the acceleration is the gravitational acceleration (g), which is approximately 9.8 m/s^2.
Since the force (F) can be calculated as F = mass * acceleration, we can express the potential energy (PE) as:
Potential Energy (PE) = Force (F) * distance (d) = mass * acceleration * height
Rearranging the formula, we find:
Height = (Potential Energy) / (mass * gravitational acceleration)
Using the Kinetic Energy calculated earlier for the potential energy, the mass of the jumper as 1 kg, and the gravitational acceleration as 9.8 m/s^2, we can find the maximum height:
Height = 25.92 Joules / (1 kg * 9.8 m/s^2) ≈ 2.65 meters
Therefore, the maximum height at which the jumper can clear the bar is approximately 2.65 meters.