An Escort and a Camaro traveling at right angles collide and stick together. The Escort has a mass of 1200 kg and a speed of 25 km/h in the positive x direction before the collision. The Camaro has a mass of 1700 kg and was traveling in the positive y direction. After the collision, the two move off at an angle of 49 o to the x axis. What was the speed of the Camaro?(in km/h)

To solve this problem, we can use the principle of conservation of momentum. Momentum is defined as the product of an object's mass and its velocity. According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

Before the collision, the Escort has a mass of 1200 kg and a velocity of 25 km/h in the positive x direction. Therefore, its momentum is calculated as:

Momentum of the Escort before the collision = Mass of the Escort * Velocity of the Escort
= 1200 kg * 25 km/h (converted to m/s)
= 1200 kg * (25 km/h * 1000 m/km) / (3600 s/h)
= 833.33 kg*m/s

Since the Camaro was traveling in the positive y direction, its velocity in the positive x direction before the collision is 0 km/h. Therefore, its momentum before the collision is:

Momentum of the Camaro before the collision = Mass of the Camaro * Velocity of the Camaro
= 1700 kg * 0 km/h (converted to m/s)
= 0 kg*m/s

After the collision, the two vehicles stick together and move off at an angle of 49 degrees to the x-axis. To find the speed of the Camaro after the collision, we need to find the total momentum after the collision and calculate its magnitude.

To calculate the total momentum after the collision, we can decompose the momentum into its x and y components using trigonometry:

Total momentum after the collision in the x direction = Total mass after the collision * Velocity after the collision in the x direction

Total momentum after the collision in the y direction = Total mass after the collision * Velocity after the collision in the y direction

Since the two vehicles stick together after the collision, the total mass after the collision is the sum of the masses of the Escort and the Camaro:

Total mass after the collision = Mass of the Escort + Mass of the Camaro
= 1200 kg + 1700 kg
= 2900 kg

The angle between the velocity after the collision and the x-axis is 49 degrees, so we can calculate the velocity after the collision in the x and y directions using trigonometry:

Velocity after the collision in the x direction = Velocity after the collision * cos(angle)
Velocity after the collision in the y direction = Velocity after the collision * sin(angle)

Now, we can rewrite the expressions for the total momentum after the collision in the x and y directions:

Total momentum after the collision in the x direction = 2900 kg * Velocity after the collision * cos(49 o)
Total momentum after the collision in the y direction = 2900 kg * Velocity after the collision * sin(49 o)

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:

Momentum of the Escort before the collision + Momentum of the Camaro before the collision = Total momentum after the collision

Plugging in the values we calculated earlier, we can solve for the velocity after the collision:

833.33 kg*m/s + 0 kg*m/s = 2900 kg * Velocity after the collision * cos(49 o)

Solving this equation will give us the velocity after the collision in the x direction. Let's call this velocity Vx.

Now, we can solve for the velocity after the collision in the y direction:

Velocity after the collision in the y direction = Total momentum after the collision in the y direction / Total mass after the collision

Since the total momentum in the y direction before the collision is 0 kg*m/s, plugging in the values we calculated earlier, we can solve for the velocity after the collision in the y direction.

Finally, we can use the Pythagorean theorem to calculate the magnitude of the velocity after the collision:

Magnitude of the velocity after the collision = sqrt((Velocity after the collision in the x direction)^2 + (Velocity after the collision in the y direction)^2)

After calculating this magnitude, we can convert it back to km/h to get the final answer.