From what height would a compact car have to be dropped to have the same kinetic energy that it has when being driven at 100 km/hr?
To find the height from which a compact car would have the same kinetic energy as it has when being driven at 100 km/hr, we can use the principle of conservation of energy.
The kinetic energy (KE) of an object can be given by the formula:
KE = (1/2) * m * v^2,
where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
Let's assume that the mass of the compact car is m.
Given that the car is being driven at a velocity of 100 km/hr, we first need to convert this to meters per second. 1 km/hr is equivalent to 1000 meters per hour, and 1 hour is equivalent to 3600 seconds. Therefore:
100 km/hr = (100000 / 3600) m/s = 27.78 m/s (approximately).
We can now calculate the kinetic energy of the car when driven at this speed.
KE = (1/2) * m * v^2
= (1/2) * m * (27.78)^2
= 384.7 * m (approximately).
Now, to find the height from which the car would need to be dropped to have this same kinetic energy, we can consider the conversion of potential energy to kinetic energy.
When the car is dropped from a height h, it gains potential energy equal to its gravitational potential energy, given by:
PE = m * g * h,
where PE is the potential energy, m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
The potential energy gained by the object is converted entirely into kinetic energy when it reaches the ground.
Therefore, we have:
PE = KE = 384.7 * m,
which implies:
m * g * h = 384.7 * m,
Simplifying,
g * h = 384.7,
h = 384.7 / g,
Substituting the value of g as 9.8 m/s^2:
h ≈ 39.339 meters (approximately).
Therefore, a compact car would need to be dropped from a height of approximately 39.339 meters to have the same kinetic energy it has when being driven at 100 km/hr.
To calculate the height from which a compact car would have to be dropped to have the same kinetic energy as when it is being driven at 100 km/hr, we need to consider the concepts of potential energy and kinetic energy.
The kinetic energy of an object can be calculated using the equation:
Kinetic Energy = (1/2) * mass * velocity^2
Where the mass is the mass of the object and the velocity is its speed.
The potential energy of an object that is elevated above the ground can be calculated using the equation:
Potential Energy = mass * gravitational acceleration * height
Where the gravitational acceleration is a constant value equal to 9.8 m/s^2 (on the surface of the Earth).
For the car to have the same kinetic energy when dropped from a certain height, the potential energy it gains while being lifted should be equal to its initial kinetic energy.
Let's break it down step by step:
1. Convert the car's velocity from km/hr to m/s.
- Divide the velocity (100 km/hr) by 3.6 to convert it to m/s.
- For example: 100 km/hr / 3.6 = 27.8 m/s (approximately)
2. Substitute the mass and velocity values into the kinetic energy equation to find the initial kinetic energy.
- Use the mass of the car, which may vary, but let's assume it to be 1000 kg (1 metric ton).
- Kinetic Energy = (1/2) * 1000 kg * (27.8 m/s)^2
- Calculate: Kinetic Energy = 387,440 Joules (approximately)
3. Set the initial kinetic energy equal to the potential energy gained during the fall.
- Potential Energy = mass * gravitational acceleration * height
- Rearrange the equation: height = Kinetic Energy / (mass * gravitational acceleration)
- Substitute the values: height = 387,440 Joules / (1000 kg * 9.8 m/s^2)
- Calculate: height ≈ 39.5 meters
Therefore, to have the same kinetic energy as when being driven at 100 km/hr, a compact car would need to be dropped from a height of approximately 39.5 meters.