To determine the initial velocity needed to achieve a high jump of 1.52 meters, we can use the principles of physics, specifically the equations of motion under the influence of gravity.
When a person jumps, they convert their initial kinetic energy into gravitational potential energy at the peak of the jump. The relationship can be described as follows:
The potential energy (PE) at the peak of the jump can be expressed as:
PE = m * g * h
Where:
- m = mass (which we will not need since it cancels out)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = maximum height (1.52 meters)
The initial kinetic energy (KE) at the takeoff can be represented as:
KE = (1/2) * m * v²
Where v is the initial velocity. Setting the kinetic energy equal to the potential energy at the maximum height gives us:
(1/2) * m * v² = m * g * h
We can cancel out the mass (m) from both sides, leading to:
(1/2) * v² = g * h
Now, we can solve for v:
v² = 2 * g * h
v = sqrt(2 * g * h)
Substituting in the known values:
g = 9.81 m/s²
h = 1.52 m
v = sqrt(2 * 9.81 * 1.52)
v = sqrt(29.87)
v ≈ 5.47 m/s
Therefore, the initial velocity required to achieve a high jump of 1.52 meters from a standing position is approximately 5.47 meters per second.