please show me in steps how to solve this
thanks alot!
A bobsled zips down an ice track, starting from rest at the top of a hill with a vertical height of 150m. Disregarding friction, what is the velocity of the bobsled at the bottom of the hill? (g=9.81 m/s^2)
any help is appreciated :)
54.2
loss of potential energy = kinetic energy at bottom
m g h = (1/2) m v^2
9.81 * 150 = (1/2) v^2
solve for v
Sure! I can help you solve this problem step-by-step.
Step 1: Determine the potential energy at the top of the hill.
Potential energy (PE) is given by the formula: PE = mgh
Where m is the mass of the bobsled, g is the acceleration due to gravity, and h is the height of the hill.
In this case, the height of the hill is given as 150m and the acceleration due to gravity is 9.81 m/s^2.
Step 2: Calculate the potential energy.
PE = mgh
PE = m * 9.81 * 150
Note: We don't have the mass of the bobsled, so we'll leave it as "m".
Step 3: Determine the kinetic energy at the bottom of the hill.
When the bobsled reaches the bottom of the hill, all the potential energy will be converted into kinetic energy.
Kinetic energy (KE) is given by the formula: KE = 0.5 * mv^2
Where m is the mass of the bobsled, and v is the velocity at the bottom of the hill.
Step 4: Equate the potential energy to the kinetic energy.
Since all the potential energy is converted into kinetic energy, we can equate the two formulas:
PE = KE
So, we get: mgh = 0.5 * mv^2
Step 5: Solve for velocity.
From the equation mgh = 0.5 * mv^2, we can cancel out mass "m" from both sides.
gh = 0.5v^2
Now, plug in the values of g (9.81 m/s^2) and h (150m):
9.81 * 150 = 0.5v^2
Step 6: Calculate.
Multiply 9.81 by 150:
1471.5 = 0.5v^2
Step 7: Solve for v.
To isolate v^2, divide both sides by 0.5:
v^2 = 1471.5 / 0.5
Step 8: Calculate.
Divide 1471.5 by 0.5:
v^2 = 2943
Step 9: Solve for v.
Take the square root of both sides to solve for v:
v = √2943
Step 10: Calculate.
Use a calculator to find the square root of 2943:
v ≈ 54.2 m/s
Therefore, the velocity of the bobsled at the bottom of the hill is approximately 54.2 m/s.
To solve this problem, we can use the principles of energy conservation. The initial potential energy (PE) at the top of the hill is converted into kinetic energy (KE) at the bottom of the hill.
The potential energy at the top of the hill is given by the equation:
PE = m * g * h
where m is the mass of the bobsled, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the hill (150m).
The kinetic energy at the bottom of the hill is given by the equation:
KE = (1/2) * m * v^2
where v is the velocity of the bobsled at the bottom of the hill.
Since the energy is conserved, we can equate the potential energy at the top of the hill to the kinetic energy at the bottom of the hill:
m * g * h = (1/2) * m * v^2
The mass of the bobsled cancels out on both sides of the equation, so we can ignore it. Rearranging the equation, we get:
v^2 = 2 * g * h
To solve for the velocity (v), follow these steps:
Step 1: Plug in the known values into the equation: v^2 = 2 * 9.81 * 150.
Step 2: Simplify the equation: v^2 = 2943.
Step 3: Take the square root of both sides to find v: v = √2943.
Step 4: Calculate the value of v using a calculator: v ≈ 54.21 m/s.
Therefore, the velocity of the bobsled at the bottom of the hill is approximately 54.21 m/s.