A 2000 kg car is rolling at 3 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay? How much energy is required to accelerate the

clay to this speed?

to stop a moving object, a force with the same magnitude should be applied at opposite direction.therefore:

momentum of car + momentum of clay = 0
momentum of car = - momentum of clay

mass of car x speed of car = mass of clay x speed of clay
speed of clay = (mass of car x speed of car) / mass of clay
speed of clay = 2000kg x 3m/s / 10kg
=600m/s

kinetic energy = momentum^2 / 2mass
=6000^2/2(10)
= 1.8 x 10^6 J

To stop the car using the sticky clay, we can use the principle of conservation of momentum. According to this principle, the initial momentum of the car and the clay will be equal to the final momentum of the car after the clay sticks to it.

The initial momentum of the car (m₁) can be calculated using the formula:

Momentum = Mass × Velocity

Given that the mass of the car (m₁) is 2000 kg and its velocity (v₁) is 3 m/s:
Initial momentum of the car (P₁) = 2000 kg × 3 m/s = 6000 kg·m/s

Now, let's assume the final velocity of the car and clay together after sticking is v₂.

The change in momentum (∆P) of the car can be calculated using the formula:

∆P = P₂ - P₁

Since the car needs to come to a stop, the final momentum (P₂) of the car and clay together will be zero:

P₂ = 0

∆P = 0 - 6000 kg·m/s
∆P = -6000 kg·m/s

The momentum of the clay (m₂) can be calculated using the formula:

Momentum = Mass × Velocity

Given that the mass of the clay (m₂) is 10 kg and its velocity (v₂) is what we need to find:
Momentum of the clay (P₂) = 10 kg × v₂

We know that ∆P (change in momentum) is equal to the difference in momentum of the clay before and after firing:

∆P = P₂ - 0

-6000 kg·m/s = 10 kg × v₂ - 0

Simplifying the equation, we have:

-6000 kg·m/s = 10 kg × v₂

Dividing both sides by 10 kg, we get:

-6000 kg·m/s ÷ 10 kg = v₂

v₂ = -600 m/s

Since velocity cannot be negative in this context, we can ignore the negative sign. Therefore, the velocity at which the clay should be fired is:

v₂ = 600 m/s

To calculate the amount of energy required to accelerate the clay to this speed, we can use the kinetic energy formula:

Kinetic Energy = 1/2 × Mass × Velocity²

Given that the mass of the clay is 10 kg and its velocity is 600 m/s:
Kinetic Energy of the clay = 1/2 × 10 kg × (600 m/s)²

Calculating further:

Kinetic Energy of the clay = 1/2 × 10 kg × 360000 m²/s²
Kinetic Energy of the clay = 1/2 × 10 kg × 360000 J
Kinetic Energy of the clay = 1800000 J

Therefore, the amount of energy required to accelerate the clay to a speed of 600 m/s is 1,800,000 Joules.