Physics...a diver of mass m drops from a board of 10m above water surface. find his speed at 5m
To find the speed of the diver at a specific height, we can make use of the principles of gravitational potential energy and kinetic energy.
1. First, let's calculate the gravitational potential energy (GPE) of the diver at the initial height of 10m. The gravitational potential energy is given by the formula:
GPE = mass * gravitational acceleration * height
In this case, the height is 10m and the mass of the diver is given as "m". The gravitational acceleration (g) is approximately 9.8 m/s².
GPE initial = m * 9.8 m/s² * 10m
2. Next, we'll calculate the gravitational potential energy at a height of 5m:
GPE final = m * 9.8 m/s² * 5m
3. Since energy is conserved, the reduction in gravitational potential energy is equal to the increase in kinetic energy. Therefore, we can equate the final gravitational potential energy to the kinetic energy:
GPE final = KE
m * 9.8 m/s² * 5m = 1/2 * m * v²
where v is the velocity or speed of the diver.
4. Solve the equation for v:
Simplifying the equation, we get:
49 m = 1/2 * v²
Multiplying by 2:
98 m = v²
Taking the square root of both sides:
v ≈ √98
v ≈ 9.9 m/s
So, the speed of the diver when they reach a height of 5m above the water surface is approximately 9.9 m/s.
To find the speed of the diver at a specific height, we can use the principle of conservation of energy.
Let's assume that the height of the water surface is at the reference level where potential energy is zero. At this reference level, the total mechanical energy of the system (diver + Earth) is conserved.
The total mechanical energy can be given as the sum of potential energy (PE) and kinetic energy (KE).
PE = mgh
KE = 1/2 mv^2
At the top of the dive, when the diver is 10m above the water surface, the potential energy is fully converted into kinetic energy. So we have:
PE_top = mgh
KE_top = 1/2 mv^2
At the height of 5m above the water surface:
PE_5m = mgh_5m
KE_5m = 1/2 mv^2_5m
According to the conservation of energy principle, the total mechanical energy at the top should be equal to the total mechanical energy at 5m. In other words, the sum of potential energy and kinetic energy at the top should be equal to the sum of potential energy and kinetic energy at the height of 5m.
PE_top + KE_top = PE_5m + KE_5m
mgh_top + 1/2 mv_top^2 = mgh_5m + 1/2 mv_5m^2
Canceling the mass (m) from both sides, we get:
gh_top + 1/2 v_top^2 = gh_5m + 1/2 v_5m^2
Since the height (h_top) at the top is given as 10m and the height (h_5m) at 5m is given as 5m, we have:
10g + 1/2 v_top^2 = 5g + 1/2 v_5m^2
Now we can solve this equation to find the speed of the diver at 5m. We know that the acceleration due to gravity (g) is approximately 9.8 m/s^2.
The mass m does not matter.
It takes about 1 second to fall 5 meters (using g=10m/s^2).
Since v = at, that means v = 10 m/s