Calculate the speed of an 90,000 kg airplane with a kinetic energy of one billion Joules.
What is the mass of a car that has a kinetic energy if 4,320,000 J moving at 23 m/s?
My answer to number 1= 149.07
second one- not sure.
I looked up the internet for formulas on finding mass and speed, (ik the KE formula)
Im just stuck on these two. I looked at my lesson and it had no explanation, only on finding KE
1. 0.5M*V^2 = KE.
0.5 * 90,000 * V^2 = 1*10^9 J. V = ?.
V = 149.07 J.
2. Use same formula as #1:
0.5M*V^2 = KE.
0.5M * 23^2 = 4.32*10^6 J. M = ?.
To calculate the speed of an airplane with a given kinetic energy:
Step 1: Use the formula for kinetic energy (KE):
KE = (1/2) * mass * velocity^2
Step 2: Rearrange the formula to solve for velocity (v):
v = sqrt((2 * KE) / mass)
Step 3: Substitute the given values into the formula:
KE = 1 billion Joules
mass = 90,000 kg
v = sqrt((2 * 1,000,000,000) / 90,000)
v = sqrt(22,222.22)
v ≈ 149.07 m/s
Your answer for the first question is correct.
To find the mass of a car with a given kinetic energy:
Step 1: Again, use the formula for kinetic energy:
KE = (1/2) * mass * velocity^2
Step 2: Rearrange the formula to solve for mass (m):
m = (2 * KE) / velocity^2
Step 3: Substitute the given values into the formula:
KE = 4,320,000 J
velocity = 23 m/s
m = (2 * 4,320,000) / (23^2)
m = 187,826.09 / 529
m ≈ 354.84 kg
Therefore, the mass of the car is approximately 354.84 kg.
To calculate the speed of an object given its kinetic energy and mass, you can use the following formula:
\[ KE = \frac{1}{2} \times m \times v^2 \]
Where:
- KE refers to the kinetic energy of the object (given in joules).
- m denotes the mass of the object (given in kilograms).
- v represents the velocity or speed of the object (in meters per second).
To answer the first question, you are given the following information:
- Mass (m) = 90,000 kg
- Kinetic Energy (KE) = 1,000,000,000 J
Plugging these values into the formula, you can solve for v:
\[ 1,000,000,000 = \frac{1}{2} \times 90,000 \times v^2 \]
Rearranging the equation:
\[ 2 \times 1,000,000,000 = 90,000 \times v^2 \]
\[ v^2 = \frac{2 \times 1,000,000,000}{90,000} \]
\[ v^2 = \frac{2,000,000,000}{90,000} \]
\[ v^2 = 22,222.22 \]
Taking the square root of both sides:
\[ v = \sqrt{22,222.22} \]
\[ v \approx 149.07 \]
So, the speed of the 90,000 kg airplane with a kinetic energy of one billion joules is approximately 149.07 m/s.
To answer the second question, you are given the following information:
- Kinetic Energy (KE) = 4,320,000 J
- Speed (v) = 23 m/s
Using the same formula, you need to solve for the mass (m):
\[ 4,320,000 = \frac{1}{2} \times m \times 23^2 \]
Rearranging the equation:
\[ 4,320,000 = 0.5 \times m \times 23^2 \]
Simplifying:
\[ m \times 529 = 4,320,000 \]
\[ m = \frac{4,320,000}{529} \]
\[ m \approx 8160.3 \]
So, the mass of the car with a kinetic energy of 4,320,000 J and a speed of 23 m/s is approximately 8160.3 kg.