A driver has 50kg mass, and drives from a high board. On entering the water the driver travels vertically downward and comes to rest in a vertical distance of 5 m. The average resistance force is acting on the driver during the motion to rest in the water is three times her weight. how high is the board?
(please show the formulas you've used..thank you)
Let F = 3*M*g be the average resistance force in the water. Let d = 5m be the vertical distance the water is penetrated. Let H = the board height above water.
Underwater net force * d = Kinetic energy entering water = Initial potential energy
(F - M*g)*d = M*g*H
2*M*g*d = M*g*H
H = 2 d = 10 m
thank youuuuu!
To solve this problem, we can use the principle of work and energy.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
Here's how we can apply the principle to find the height of the board:
1. Start by finding the gravitational potential energy of the driver before entering the water. The potential energy can be calculated using the formula:
Potential Energy = mass * gravity * height
Given that the mass of the driver is 50 kg and the acceleration due to gravity is approximately 9.8 m/s², we have:
Potential Energy = 50 kg * 9.8 m/s² * H1 (height of the board)
2. Next, we need to calculate the work done by the resistance force during the driver's descent. The work done is given by:
Work = force * displacement * cos(angle)
In this case, the force is 3 times the driver's weight, which can be calculated by multiplying the mass (50 kg) by the acceleration due to gravity (9.8 m/s²). Therefore, the force is:
Force = 3 * 50 kg * 9.8 m/s²
The displacement is the vertical distance traveled by the driver, which is given as 5 m. The angle between the force and the displacement is 0 degrees (cos(0) = 1).
3. Using the work-energy principle, we can equate the initial potential energy to the work done during descent:
Potential Energy = Work
Plugging in the values we calculated:
50 kg * 9.8 m/s² * H1 = 3 * 50 kg * 9.8 m/s² * 5 m
4. Simplify and solve the equation for H1:
H1 = (3 * 50 kg * 9.8 m/s² * 5 m) / (50 kg * 9.8 m/s²)
The mass and acceleration due to gravity cancel out, leaving us with:
H1 = 3 * 5 m
H1 = 15 m
Therefore, the height of the board is 15 meters.