A 2137 kg car moving east at 12.91 m/s collides with a 3264 kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 36.8 ◦ north of east and at a speed of 6.38 m/s. What was the speed of the 3264 kg car before the collision? Answer in units of m/s.

The speed of the 3264 kg car before collision is 6.32 m/s

Explanation:

Let first car, mass m₁, moving east be moving with velocity, v₁ and second car, mass m₂, moving north be moving with velocity, v₂. Let the velocity of the two cars after collision be v₃

In a Collison (whether elastic or inelastic), momentum is always conserved.

Momentum before collision = momentum after collision.

Momentum before collision = m₁v₁ + m₂v₂

v₁ = (12.91î) m/s in vector form, m₁ = 2137 kg

v₂ = ?, v₂ = (v₂j) m/s in vector form, m₂ = 3264 kg

Momentum before collision = (2137)(12.91î) + (3264)(v₂j) = (27590î + 3264v₂j) kgm/s

Momentum after collision = (total mass of the cars after collision) × (velocity of the stuck-together cars after collision)

Total mass of the cars after collision = m₁ + m₂ = 2137 + 3264 = 5401 kg

Velocity after collision, v₃ = 6.38 m/s In the N36.8°E direction, put in vector form,

v₃ = (6.38 cos 36.8°î + 6.38 sin 36.8°j)

v₃ = (5.11î + 3.82j) m/s

Momentum after collision = 5401 (5.11î + 3.82j) = (27590î + 20641.4j) kgm/s

Momentum before collision = momentum after collision.

(27590î + 3264v₂j) = (27590î + 20641.4j)

Comparing components

3264v₂ = 20641.4j

v₂ = 6.32 m/s

Hope this Helps!!!

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

attach the statements so i can answer : )