a man weighs 13 stone, he jumps into water from a height of 50ft, how deep into the water would he go?
To determine how deep the man would go into the water, we need to consider the impact of the jump and his weight. The key factor for this calculation is the concept of density—the relationship between mass and volume.
To get the answer, we can follow these steps:
Step 1: Convert the man's weight from stone to kilograms.
- 1 stone is equal to 6.35 kilograms, so we multiply 13 stone by 6.35 to convert it to kilograms.
- 13 stone * 6.35 kg/stone = 82.55 kilograms (rounded to the nearest hundredth).
Step 2: Calculate the potential energy of the man using his weight and the height from which he jumps.
- Potential energy (PE) is given by the formula: PE = mass * gravity * height.
- The acceleration due to gravity is approximately 9.8 meters per second squared.
- The height is given as 50 feet, so we need to convert it to meters by multiplying by 0.3048 (1 foot = 0.3048 meters).
- PE = 82.55 kg * 9.8 m/s² * (50 ft * 0.3048 m/ft) = 12301 joules.
Step 3: Calculate the depth into the water using the principle of conservation of energy.
- The potential energy of the man at the top of his jump is entirely converted into kinetic energy (KE) as he hits the water.
- KE = PE
- KE = 1/2 * mass * velocity²
- We can solve for the velocity using the formula: velocity = sqrt((2 * KE) / mass)
- Since KE = PE, we can rewrite it as: velocity = sqrt((2 * PE) / mass)
- velocity = sqrt((2 * 12301 J) / 82.55 kg) = 10.9 m/s (rounded to the nearest tenth).
Step 4: Use the velocity to determine the depth the man would go into the water.
- The depth can be calculated using the formula: depth = (velocity²) / (2 * acceleration due to gravity)
- acceleration due to gravity = 9.8 m/s²
- depth = (10.9 m/s)² / (2 * 9.8 m/s²) = 6.03 meters (rounded to the nearest hundredth).
Therefore, the man would go approximately 6.03 meters deep into the water.