Answer :
Answer:
The mass of the first car is 1498.31 kg.
Explanation:
Given that,
Initial speed of an automobile, [tex]u_1=66.9\ km/h = 18.58\ m/s[/tex]
Initial speed of the car is 0 as it is at rest, [tex]u_2=0[/tex]
After the collision, the two cars lock up and they slide together with a speed of, V = 36.1 km/h = 10.02 m/s
The mass of the parked car, [tex]m_2=1280\ kg[/tex]
We need to find the mass of the first car. It is a case of inelastic collision in which two objects stick together. The conservation of momentum follows here. So,
[tex]m_1u_1+m_2u_2=(m_1+m_2)V\\\\m_1u_1=(m_1+m_2)V\\\\m_1u_1=(m_1+m_2)V[/tex]
[tex]m_1[/tex] is the mass of the first car
After rearranging we get :
[tex]m_1=\dfrac{m_2V}{u_1-V}\\\\m_1=\dfrac{1280\times 10.02}{18.58-10.02}\\\\m_1=1498.31\ kg[/tex]
So, the mass of the first car is 1498.31 kg. Hence, this is the required solution.
Use the principle of conservation of momentum to solve the problem and determine the mass of the sliding car.
To solve this problem, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. We can calculate the momentum of the sliding car using the equation:
Momentum = mass * velocity
Using the given velocities and the mass of the parked car, we can determine the mass of the sliding car.
First, we convert the velocities to m/s:
- 66.9 km/h = 18.6 m/s
- 36.1 km/h = 10.0 m/s
Next, we calculate the momentum of the parked car:
momentum_parked_car = mass_parked_car * velocity_parked_car
Plugging in the given values:
momentum_parked_car = 1280 kg * 10.0 m/s
Now, we can determine the mass of the sliding car using:
momentum_sliding_car = (mass_parked_car + mass_sliding_car) * velocity_after_collision
Plugging in the given values:
(1280 kg + mass_sliding_car) * 10.0 m/s = (mass_parked_car + mass_sliding_car) * 18.6 m/s
We can solve this equation to find the mass of the sliding car.
Learn more about conservation of momentum here:
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