Two automobiles, each of mass 1000kg , are moving at the same speed, 17m/s , when they collide and stick together.

At what speed does the wreckage move if one car was driving north and one east?

before

x momentum = 17,000 (east)
y momentum = 17,000 (north)
after
m Vx = 2000 V cos T = 17,000 still
m Vy = 2000 V sin T = 17,000 still

so
sin T = cos T so T = 45 deg and sin = cos =sqrt2 /2

2000 V (sqrt 2/2) = 17,000
V = 17 /sqrt 2 = 12 m/s

Well, when the two cars collide, it's no longer a matter of going north or east. It becomes a matter of "where the heck are we going now?" I can imagine the wreckage moving in a kind of confused, zigzag pattern at a whopping speed of "Whoa, slow down, hotshot, we're all stuck together now!"

To find the speed of the wreckage after the collision, we can use the concept of conservation of momentum.

The momentum of an object is given by the product of its mass and velocity. Since the two cars stick together after the collision, their total momentum before the collision should be equal to the total momentum after the collision.

Given:
Mass of each car = 1000 kg
Velocity of each car = 17 m/s (assuming towards north and east directions)

1. Calculate the momentum of each car before the collision:
Momentum of car 1 = mass of car 1 x velocity of car 1
= 1000 kg x 17 m/s = 17000 kg·m/s (towards north)

Momentum of car 2 = mass of car 2 x velocity of car 2
= 1000 kg x 17 m/s = 17000 kg·m/s (towards east)

2. Calculate the total momentum before the collision:
Total momentum before collision = Momentum of car 1 + Momentum of car 2

= 17000 kg·m/s + 17000 kg·m/s = 34000 kg·m/s

3. Since the cars stick together after the collision, the total momentum after the collision is the same as before the collision.

4. To find the velocity of the wreckage, we need to divide the total momentum after the collision by the total mass of the wreckage (which is the sum of the masses of the two cars):

Total mass of the wreckage = mass of car 1 + mass of car 2
= 1000 kg + 1000 kg = 2000 kg

5. Calculate the velocity of the wreckage:
Velocity of the wreckage = Total momentum after the collision / Total mass of the wreckage

= 34000 kg·m/s / 2000 kg

= 17 m/s

Therefore, the wreckage moves at a speed of 17 m/s (assuming towards north-east direction) after the collision.

To determine the speed at which the wreckage moves, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

First, let's determine the total initial momentum before the collision. The momentum of an object is calculated by multiplying its mass by its velocity. Since both cars have the same mass (1000 kg) and are moving at the same speed (17 m/s), their momenta are the same.

Therefore, the total initial momentum before the collision is the sum of the individual momenta of the two cars:
P_initial = (mass_car1 * velocity_car1) + (mass_car2 * velocity_car2)

In this case, car 1 is moving north, so its velocity can be written as 0 m/s in the eastward direction and 17 m/s in the northward direction. Car 2 is moving east, so its velocity can be written as 17 m/s in the eastward direction and 0 m/s in the northward direction.

P_initial = (1000 kg * 0 m/s) + (1000 kg * 17 m/s)

Next, let's determine the total final momentum after the collision. Since the cars collide and stick together, the wreckage will move as a single unit. Therefore, its mass will be the sum of the masses of the individual cars (2 * 1000 kg) and the velocity of the wreckage will be our unknown value, which we'll call V_wreckage.

P_final = (mass_wreckage * V_wreckage)

According to the law of conservation of momentum, P_initial = P_final. Therefore, we can equate the initial and final momenta and solve for V_wreckage:

(mass_car1 * velocity_car1) + (mass_car2 * velocity_car2) = (mass_wreckage * V_wreckage)

Substituting the known values:
(1000 kg * 0 m/s) + (1000 kg * 17 m/s) = (2000 kg * V_wreckage)

Now, we can solve for V_wreckage:
17000 kg m/s = 2000 kg * V_wreckage

V_wreckage = 17000 kg m/s / 2000 kg

V_wreckage = 8.5 m/s

Therefore, the wreckage moves at a speed of 8.5 m/s.