Assuming the best high jump record from a standingposition in a school was 1.52 m, what initial velocity was needed for this jump? Neglect any sideways motion.

The minimum initial velocity will create at least the kinetic energy (1/2)mv² to equal the potential energy gained, mgh, where h is the height difference between the horizontal rod and the cg of the person from the ground.

Make assumptions to the value of this difference, knowing that most high-jumpers put the body to a slant or even horizontal at the critical moment.

To find the initial velocity needed for the high jump, we can use the principles of projectile motion. The key is to know that the vertical motion of the jumper can be treated as a projectile, where the only force acting on the jumper is gravity.

Let's break down the problem into different steps to find the initial velocity:

Step 1: Identify the known quantities:
- The best high jump record from a standing position: 1.52 m
- The acceleration due to gravity (g): Approximately 9.8 m/s² (neglecting air resistance)

Step 2: Determine the equations to use:
We will use the kinematic equation that relates displacement, initial velocity, time, and acceleration in the vertical direction:

Δy = v₀y * t + (1/2) * g * t²

Where:
Δy = Displacement in the vertical direction (1.52 m)
v₀y = Initial vertical velocity (what we want to find)
t = Time the jump takes (unknown)
g = Acceleration due to gravity (9.8 m/s²)

Step 3: Solve for the initial velocity:
Since the high jump is a vertical motion, the final vertical displacement is zero (the jumper ends up back on the ground). Therefore, we can rearrange the equation as follows:

0 = v₀y * t + (1/2) * g * t²

Since the initial jump is from a standing position, the initial vertical velocity (v₀y) is zero. Thus, the equation simplifies to:

0 = (1/2) * g * t²

Step 4: Solve for time:
Rearrange the equation to solve for time (t):

t = sqrt(2Δy / g)

Substitute the given values:

t = sqrt(2 * 1.52 / 9.8)

Step 5: Calculate the time:
Using a calculator, evaluate the expression:

t ≈ 0.559 seconds

Step 6: Calculate the initial velocity:
Now that we have the time (t), we can substitute it into the original equation to find the initial velocity (v₀y):

Δy = v₀y * t + (1/2) * g * t²

Substitute the known values:

1.52 = v₀y * 0.559 + (1/2) * 9.8 * 0.559²

Simplify and solve for v₀y:

v₀y ≈ 5.28 m/s

Therefore, to achieve the high jump record of 1.52 meters from a standing position, an initial vertical velocity of approximately 5.28 m/s is needed.