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kumpel
2 months ago
9

You are an investigator at the scene of a car crash. A Volvo of has hit an Alpha Romeo from the side and the two are inter-tangl

ed (stuck together). You can see that the Volvo was traveling due east on a concrete road with a 50 mph speed limit and made a 30.0 m long skid mark before reaching the intersection where it hit the Alpha Romeo which was driving due North on a concrete road with a 25 mph speed limit. There are additional skid marks from both cars that are 12.25 m long at 15 degrees North of East. Further investigation tells you that the mass of the Volvo (including the driver) is 1650 kg and the mass of the Alpha Romeo (including the driver) is 975 kg. Your task is to determine if either car was speeding. 1. Determine the speed of the Volvo before it slammed on the brakes. 2. Find the speed of the Alpha Romeo when it was hit by the Volv
Physics
2 answers:
serg [3.5K]2 months ago
5 0

Answer:

Let the Volvo's speed upon braking be v, and its mass be m1.

The speed of the Volvo just before the crash is represented as v1.

After applying the brakes, the skidding distance is noted as 30 m.

The equation governing this scenario is v1^2- v^2 = - 2 * a * s, where a= represents deceleration and s= denotes skidding distance.

Assuming the deceleration to be -0.3 g = - 2.94 m/s^2 (as provided by the Volvo website for the car's emergency system).

The equation can be modified to solve for v: v^2 = v1^2 + (2 * a * s )= v1^2 + 176.4.

After the collision, both vehicles merge and proceed together (m1+m2) at an initial speed of V (let's say).

They then move 12.25 m and eventually come to a stop.

Using the equation (0)^2 -(V)^2 = - 2 * a' * s', where a' signifies the combined deceleration and s' denotes the distance traveled by the two cars.

Let's assume the combined system’s deceleration is notably higher at (- g).

Utilizing the format V^2 = 2 * 9.8 * 12.25.

This results in V = 15.5 m/s.

Using momentum conservation in the X direction (East): m1 * v1 = (m1+ m2) * V * cos 15.

Solving for v1 gives: v1 = (1650+ 975) Kg * 15.5 m/s * cos 15 /1650 Kg = 23.8 m/s.

Hence, v^2 = V1^2 + 176.4 = (23.8)^2 + 176.4.

This results in v = 27.3 m/s = 61.1 mph (indicating that he exceeded the speed limit when applying the brakes).

In the Y-direction momentum conservation shows: m2 * v2 = (m1+m2) * V * sin 15.

Solving for v2 results in: v2 = (m1+m2) * V * sin 15/m2.

We conclude with v2 = 41.7 m/s (93.3 m/hr) indicating he also exceeded the speed limit.

serg [3.5K]2 months ago
4 0

Answer:

1. The speed of the Volvo is 27.3 m/s

2. The speed of the Alpha Romeo is 10.8 m/s

Explanation:

1. Parameters given:

v = the speed of the Volvo

m₁ = the mass of the Volvo

v₁ = the speed of the Volvo prior to collision

Distance during skidding = 30 m

v_{1} ^{2} -v^{2} =-2a*s

Where a denotes deceleration = -2.94 m/s²

To solve for v

v^{2} =v_{1} ^{2} +176.4

Following the collision, both cars travel as one, thus

0-V^{2} =-2*a*s\\V=\sqrt{2as} =\sqrt{2*9.8*12.25} =12.25m/s

The momentum conservation in the X direction is then:

v_{1} =\frac{(m_{1}+m_{2})*V*cos15 }{m_{1} } =\frac{(1650+975)*15.5*cos15}{1650} =23.8m/s

v=\sqrt{v_{1}^{2}+176.4 } =\sqrt{23.8^{2}+176.4 } =27.3m/s

2. The momentum conservation in the Y direction gives:

v_{2} =\frac{(m_{1}+m_{2})*V*sin15 }{m_{2} } =\frac{(1650+975)*15.5*sin15}{975} =10.8m/s

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