2 cars of equal mass m collide at an intersection. Driver E traveled eastward and driver N northward. After the collision, 2 cars remain joined together and slide, before coming to a rest. Police measured the skid mark length d to be 9metres. Coefficient of friction is 0.9. based on the skid marks find the 2 joined cars speed.

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To find the initial speed of the two joined cars before the collision, we can make use of the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.

Let's denote the initial speed of Driver E's car as VE and the initial speed of Driver N's car as VN. Since the two cars were initially moving perpendicular to each other, their momenta will be perpendicular as well.

The momentum of an object is given by the product of its mass and velocity. Since the two cars have equal mass m, their momenta before the collision can be expressed as:

Momentum of E: PE = m * VE
Momentum of N: PN = m * VN

After the collision, the two cars remain joined together and slide before coming to a rest. In this case, their final velocity will be zero. Therefore, the total momentum after the collision is zero:

Total momentum after collision: PT = 0

According to the conservation of momentum principle, the total momentum before the collision (PE + PN) is equal to the total momentum after the collision (PT). So we have:

PE + PN = PT
m * VE + m * VN = 0

Since the two cars remain joined together, their masses and the coefficient of friction do not affect the final calculation of their initial speed. Thus, we can solve for VE by rearranging the equation:

VE = - VN

So the initial speed of Driver E's car can be determined by taking the negative of the initial speed of Driver N's car.

Now, let's focus on determining the initial speed of Driver N's car (VN). To find VN, we need to make use of the skid mark length (d) and the coefficient of friction (μ).

The skid mark length (d) can be related to the initial speed of the cars using the equations of motion. In this case, since the cars come to a rest, we can use the equation:

v^2 = u^2 - 2as

Where:
v = final velocity (0 m/s)
u = initial velocity (VN m/s)
a = acceleration (friction force)
s = displacement (d meters)

Rearranging the equation, we have:

u^2 = v^2 + 2as
u^2 = 0^2 + 2 * μ * g * d

Since the coefficient of friction (μ) is given as 0.9 and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can substitute these values into the equation:

u^2 = 0 + 2 * 0.9 * 9.8 * 9

Simplifying further, we find:

u^2 = 158.04

Taking the square root of both sides, we get:

u ≈ 12.57

Therefore, the initial speed of Driver N's car (VN) is approximately 12.57 m/s.

Since VE = - VN, the initial speed of Driver E's car is -12.57 m/s.

Thus, the two joined cars had an initial speed of approximately -12.57 m/s.