A person with a mass of 60kg climbs up to a diving board 4 meters above a swimming pool. what is the divers speed when entering the water?
A 8.9m/s
b 6.2m/s
c 4.4m/s
d 3.3m/s
e 2.1 m/s
Ans. A
PE =KE
m•g•h = m•v²/2
v =sqrt (2•g•h) =
sqrt(2•9.8•4) = 8.9 m/s
To determine the diver's speed when entering the water, we can use the principles of physics, specifically the conservation of energy.
First, let's calculate the potential energy of the diver at the diving board using the formula:
Potential Energy (PE) = mass (m) x acceleration due to gravity (g) x height (h)
Given:
mass (m) = 60kg
acceleration due to gravity (g) = 9.8 m/s^2
height (h) = 4m
PE = 60kg x 9.8 m/s^2 x 4m
= 2352 Joules
According to the law of conservation of energy, the potential energy of the diver at the diving board will be converted into kinetic energy when entering the water. The kinetic energy can be calculated using the formula:
Kinetic Energy (KE) = 1/2 x mass (m) x velocity^2
Since the diver is initially at rest, the initial kinetic energy is zero. Therefore, we can equate the potential energy to the final kinetic energy:
PE = KE
2352 J = 1/2 x 60kg x velocity^2
Simplifying the equation:
4704 J = 60kg x velocity^2
Dividing both sides by 60kg and taking the square root:
78.4 m^2/s^2 = velocity^2
Velocity = √(78.4 m^2/s^2)
Velocity ≈ 8.85 m/s
Rounding to one decimal place, the diver's speed when entering the water is approximately 8.9 m/s.
Therefore, the correct answer is option A) 8.9 m/s.