a car of mass 500kg is moving at 24m/s . a lion of mass 100kg drops on to the roof of the car from an overhanging branch. show that the car will slow down to 20m/s.
Well, that lion must have some serious pounce power! Let's calculate what happens when the lion lands on the car.
We can start by using the conservation of momentum. The initial momentum of the car before the lion lands is given by the equation:
(initial mass of the car) x (initial velocity of the car) = (final mass of the car) x (final velocity of the car)
Before the lion lands:
(500 kg) x (24 m/s) = (500 kg + 100 kg) x (final velocity of the car)
Simplifying the equation:
12000 kg·m/s = 600 kg x (final velocity of the car)
To find the final velocity, we rearrange the equation:
(final velocity of the car) = (12000 kg·m/s) / (600 kg)
(final velocity of the car) = 20 m/s
So, with that lion dropping onto the car, it slows down to a final velocity of 20 m/s. It seems like that lion's got a knack for slowing things down, doesn't it?
To show that the car will slow down to 20 m/s after the lion drops onto the roof, we will use the principle of conservation of momentum.
1. Calculate the initial momentum of the car:
Momentum (p) = mass (m) * velocity (v)
Initial momentum of the car = 500 kg * 24 m/s = 12000 kg·m/s
2. Calculate the initial momentum of the lion:
Initial momentum of the lion = 100 kg * 0 m/s (since it was initially at rest) = 0 kg·m/s
3. Calculate the total initial momentum before the lion drops onto the car:
Total initial momentum = Initial momentum of the car + Initial momentum of the lion
Total initial momentum = 12000 kg·m/s + 0 kg·m/s = 12000 kg·m/s
4. Calculate the final momentum after the lion drops onto the car:
Final momentum = Total initial momentum
Final momentum = 12000 kg·m/s
5. Calculate the final velocity of the car after the lion drops onto the roof:
Final velocity (v') = Final momentum (p') / mass (m')
The total mass after the lion drops onto the car will be the sum of the car's mass and the lion's mass:
Total mass after the lion drops = Car's mass + Lion's mass
Total mass after the lion drops = 500 kg + 100 kg = 600 kg
Final velocity of the car = 12000 kg·m/s / 600 kg = 20 m/s
Thus, the car will slow down to 20 m/s after the lion drops onto the roof.
To show that the car will slow down to 20 m/s, we need to apply the law of conservation of momentum. The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
Let's calculate the initial momentum of the car and lion before the lion drops on the car.
The initial momentum of an object is given by the product of its mass and velocity:
Initial momentum of the car = mass of the car × velocity of the car = 500 kg × 24 m/s = 12000 kg·m/s
Initial momentum of the lion = mass of the lion × velocity of the lion = 100 kg × 0 m/s (since the lion is initially at rest) = 0 kg·m/s
Now, let's calculate the momentum of the car and lion after the lion drops on the car.
The final momentum of the car and lion can be obtained by adding up their individual momenta:
Final momentum of the car and lion = momentum of the car + momentum of the lion
The momentum of an object can also be calculated as the product of its mass and velocity:
Final momentum of the car and lion = (mass of the car + mass of the lion) × final velocity of the car and lion
Now, we need to solve for the final velocity of the car and lion.
Using the law of conservation of momentum, we can equate the initial momentum to the final momentum:
Initial momentum of the car = Final momentum of the car and lion
Therefore,
12000 kg·m/s = (500 kg + 100 kg) × final velocity of the car and lion
Simplifying the equation:
12000 kg·m/s = 600 kg × final velocity of the car and lion
Dividing both sides of the equation by 600 kg:
20 m/s = final velocity of the car and lion
Thus, the final velocity of the car and lion after the lion drops on the car is 20 m/s, showing that the car will slow down to 20 m/s.