Question

Roughly how deep would a 200 pound person go into the water if they hit at terminal velocity and in a standard hands-first dive position?

Answer 1

Determining the exact depth a person would reach upon hitting the water at terminal velocity is a complex problem that depends on various factors, such as body position, water entry angle, and the person's specific characteristics (e.g., surface area, drag coefficient). However, I can provide a rough estimate based on some assumptions.

Assuming a person in a standard hands-first dive position with a mass of 200 pounds (approximately 90.7 kilograms) and neglecting air resistance, we can consider the following:

1. Terminal Velocity: The terminal velocity of a person in a dive position is estimated to be around 53 m/s (174 ft/s) or roughly 190 km/h (118 mph). This assumes a streamlined body position and typical values for drag coefficients.

2. Water Entry: When a person enters the water, they experience deceleration due to drag forces acting against their motion. The deceleration upon hitting the water depends on factors such as entry angle, body position, and water density.

3. Depth Estimate: To estimate the depth reached, we assume a constant deceleration during the water entry. An average deceleration value used for this estimation is around 12 m/s² (39 ft/s²).

Based on these assumptions, we can use basic kinematic equations to estimate the depth reached by the person. Using the kinematic equation:

$d=\frac{v^2}{2a}$

where: d = depth reached v = initial velocity (terminal velocity) a = deceleration

Plugging in the values:

$d=\frac{(53\text{m/s}{)}^2}{2\cdot 12{\text{m/s}}^2}\approx 117\text{meters}$

So, based on these rough estimates, a 200-pound person diving at terminal velocity in a standard hands-first position would roughly reach a depth of around 117 meters (384 feet) upon hitting the water. However, please note that this estimation is simplified and may not accurately reflect real-world scenarios, as many factors can affect the outcome.