Hi! I have a problem for physics homework and I though I knew how to solve it but apparently it is wrong, please help!
'Two cars, one of mass 1000 kg, and the second of mass 2400 kg, are moving at right angles to each other when they collide and stick together. The initial velocity of the first car is 11 m/s in the positive x direction and that of the second car is 19 m/s in the positive y direction.
What is the magnitude of the velocity of the wreckage of the two crs immediately after the collision? Answer in units of m/s"
I did (1000*11)+(2400*19)=3400*v3
is that correct?
You forgot to include the directions of the speeds. The correct equation is:
1000*11 x-hat +2400*19 y-hat=3400*v3
v3 = 110/43 x-hat +24*19/43 y-hat
The magnitude of v3 is thus:
sqrt[(110/43 )^2 + (24*19/43 )^2]
I wonder if Count Iblis transposed 34 to 43? Check my thinking.
so does 10.908 sound right?
Also, ( just so I know for future problem) what is x-hat and y-hat (we just started 2d collisions so I am sorry if this is very obvious)
xhat and y hat are unit direction vectors, of magnitude 1. Thus 12xhat is 12 in the x direction.
To correctly solve this problem, you need to apply the principles of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. The problem states that the cars stick together after the collision, meaning they move as one combined object.
Let's break down the steps to solve the problem:
Step 1: Calculate the momentum of each car before the collision. Momentum is defined as mass multiplied by velocity.
Momentum of the first car (p1) = mass of the first car (m1) * velocity of the first car (v1)
p1 = 1000 kg * 11 m/s
Momentum of the second car (p2) = mass of the second car (m2) * velocity of the second car (v2)
p2 = 2400 kg * 19 m/s
Step 2: Calculate the total momentum before the collision (p_total) by adding the individual momenta of both cars.
p_total = p1 + p2
Step 3: Calculate the velocity of the wreckage (v3) after the collision. Since the cars stick together, their combined mass is the sum of the individual masses.
Total mass after the collision (m_total) = m1 + m2
Using the principle of conservation of momentum, the total momentum after the collision (p_total) is equal to the mass of the wreckage (m_total) multiplied by its velocity (v3).
p_total = m_total * v3
Step 4: Rearrange the equation and solve for v3.
v3 = p_total / m_total
Now, let's apply these steps to your problem:
Step 1: Calculate the momentum of each car before the collision.
p1 = 1000 kg * 11 m/s = 11000 kg·m/s
p2 = 2400 kg * 19 m/s = 45600 kg·m/s
Step 2: Calculate the total momentum before the collision.
p_total = p1 + p2
p_total = 11000 kg·m/s + 45600 kg·m/s = 56600 kg·m/s
Step 3: Calculate the velocity of the wreckage after the collision.
m_total = m1 + m2
m_total = 1000 kg + 2400 kg = 3400 kg
Step 4: Solve for v3.
v3 = p_total / m_total
v3 = 56600 kg·m/s / 3400 kg ≈ 16.65 m/s
Therefore, the magnitude of the velocity of the wreckage immediately after the collision is approximately 16.65 m/s.