A 14000 N automobile travels at a speed of 40 km/h northward along a street, and a 7000 N sports car travels at a speed of 62 km/h eastward along an intersecting street.(a) If neither driver brakes and the cars collide at the intersection and lock bumpers, what will the velocity of the cars be immediately after the collision?

(b) What percentage of the initial kinetic energy will be lost in the collision?

No, not hard, conservation of momentum

Initial north momentum =
(14000 N/9.81 m/s^2) (40000m/3600 s)

Initial east momentum =
(7000/9.81)(62000/3600)

Final north and east momentums are the same
total mass = m = 21000/9.81
m v cos T = initial east momentum
m v sin T = initial north momentum
solve for T, the angle up from east axis
then get v, the speed
Vnorth = v sin T
Veast = v cos T

Final ke = (1/2) m v^2
initial ke = (1/2)m1 initial speed1 ^2 + (1/2) m2 initial speed2^2

To solve this problem, we need to use the principle of conservation of momentum and the concept of kinetic energy.

a) To find the velocity of the cars after the collision, we need to use the conservation of momentum. The momentum before the collision should be equal to the momentum after the collision.

Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). In this case, we have two objects, the automobile and the sports car. Let's assume the automobile (car A) has a mass of m1 and the sports car (car B) has a mass of m2.

The momentum before the collision is given by:

m1 * v1_initial + m2 * v2_initial

Where:
m1 = mass of the automobile
v1_initial = initial velocity of the automobile (northward)
m2 = mass of the sports car
v2_initial = initial velocity of the sports car (eastward)

The momentum after the collision is given by:

(m1 + m2) * v_final

Where:
v_final = final velocity of both cars after the collision

According to the conservation of momentum, the two equations should be equal:

m1 * v1_initial + m2 * v2_initial = (m1 + m2) * v_final

Now we substitute the given numerical values in the equation. The automobile has a mass greater than the sports car, so we can label car A as the automobile and car B as the sports car.

m1 = mass of the automobile = 14000N / 9.8 m/s^2 (acceleration due to gravity)
m2 = mass of the sports car = 7000N / 9.8 m/s^2 (acceleration due to gravity)
v1_initial = velocity of the automobile = 40 km/h * 1000 m/km / 3600 s/hr = 11.11 m/s (northward)
v2_initial = velocity of the sports car = 62 km/h * 1000 m/km / 3600 s/hr = 17.22 m/s (eastward)

Substituting the values into the equation:

(14000 /9.8) * 11.11 + (7000 / 9.8) * 17.22 = (14000 / 9.8 + 7000 / 9.8) * v_final

Now solve for v_final to get the velocity after the collision.

b) To find the percentage of the initial kinetic energy lost in the collision, we need to compare the initial kinetic energy (KE_initial) with the final kinetic energy (KE_final) after the collision.

The kinetic energy of an object is given by the formula:

KE = (1/2) * m * v^2

Where:
m = mass of the object
v = velocity of the object

The initial kinetic energy is given by:

KE_initial = (1/2) * m1 * v1_initial^2 + (1/2) * m2 * v2_initial^2

The final kinetic energy is given by:

KE_final = (1/2) * (m1 + m2) * v_final^2

Now we substitute the given numerical values into the equations and solve for the percentages.

Final velocity = v_final
Initial velocity of car A = v1_initial
Initial velocity of car B = v2_initial

KE_initial = (1/2) * m1 * v1_initial^2 + (1/2) * m2 * v2_initial^2
KE_final = (1/2) * (m1 + m2) * v_final^2

To find the percentage of energy lost, we need to calculate the difference between the initial and final kinetic energies, and then divide it by the initial kinetic energy:

Percentage of energy lost (%) = [(KE_initial - KE_final) / KE_initial] * 100