Physics: A car is parked on an icy hill inclined at 10°, when it begins to slide. What is the car's speed at the bottom of the 155-m hill?:
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To find the car's speed at the bottom of the hill, we can use the principle of conservation of mechanical energy. At the top of the hill, the car has potential energy (due to its height) and no kinetic energy (since it is not moving). At the bottom of the hill, the car will have maximum kinetic energy and no potential energy. Assuming no frictional forces are acting on the car, the mechanical energy is conserved.
The potential energy at the top of the hill can be calculated using the formula:
PE = m * g * h
where PE is the potential energy, m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the hill.
Since the car is parked and not moving, its initial kinetic energy is zero.
Therefore, at the bottom of the hill, the total mechanical energy (potential energy + kinetic energy) is equal to the initial potential energy:
PE = KE
To find the speed at the bottom of the hill, we can equate the potential energy to the kinetic energy and solve for the speed:
m * g * h = (1/2) * m * v^2
where v is the velocity/speed of the car.
Simplifying the equation, we get:
v^2 = 2 * g * h
Finally, taking the square root of both sides, we get:
v = sqrt(2 * g * h)
Plugging in the values:
v = sqrt(2 * 9.8 * 155)
v ≈ 38.5 m/s
Therefore, the car's speed at the bottom of the 155-m hill is approximately 38.5 m/s.
To determine the car's speed at the bottom of the hill, we can use the principle of conservation of energy.
Here's how you can calculate it:
1. Start by finding the height of the hill with respect to the bottom. Since the car is parked on the hill, the height is given by the vertical distance between the car's initial position and the bottom of the hill. Use trigonometry to find this height:
height = 155 m * sin(10°)
2. Next, calculate the initial potential energy of the car. This is the energy possessed by the car due to its position on the hill. The potential energy is given by:
potential energy = mass * gravity * height
Here, 'mass' refers to the mass of the car, 'gravity' is the acceleration due to gravity (approximately 9.8 m/s^2), and 'height' is the value we calculated in step 1.
3. Now, determine the final kinetic energy of the car at the bottom of the hill. As the car slides down, the potential energy is converted into kinetic energy. The kinetic energy is given by:
kinetic energy = (1/2) * mass * velocity^2
'velocity' represents the car's speed at the bottom of the hill, which is what we're trying to find.
4. Since energy is conserved, equate the potential energy calculated in step 2 to the kinetic energy calculated in step 3:
potential energy = kinetic energy
Substitute the expressions for potential energy and kinetic energy from steps 2 and 3 accordingly.
5. Solve the equation to find the velocity (speed):
(1/2) * mass * velocity^2 = mass * gravity * height
By canceling out the mass factor, the equation simplifies to:
(1/2) * velocity^2 = gravity * height
Rearrange the equation to solve for velocity:
velocity = √(2 * gravity * height)
6. Substitute the values for 'gravity' (9.8 m/s^2) and the calculated 'height' (from step 1) into the equation from step 5. Finally, calculate the velocity to find the car's speed at the bottom of the hill.