Question

(PLEASE ANSWER, 50 PTS) On an icy day, a police officer was using his radar gun to catch speeding cars when he witnessed a rear-end collision. The officer drew a diagram of the accident in his police report. A reproduction of it is shown below. In the diagram, each car is represented by a box labeled with the appropriate letter. Car C represents the police officer. There is also some data that has been collected by a team of lawyers hired by the driver of Car A. The driver of Car A claims that he was not speeding at the time of the collision.

Based on the information the officer collected at the scene of the crime write a scientific explanation that determines whether or not Car A was speeding when it collided with Car B.

Answer 1

Based on the conservation of momentum, we can determine that Car A was traveling at a speed of 31.7 mph before the collision. The speed limit is 35 mph, so Car A was not speeding at the time of the collision.

To determine whether or not Car A was speeding when it collided with Car B, we can use the following scientific explanation:

Conservation of momentum: Momentum is the product of an object's mass and velocity. In a closed system, momentum is conserved, meaning that the total momentum of all objects in the system remains constant before and after a collision.

Formula for momentum:

momentum = mass * velocity

Applying conservation of momentum to the collision of Car A and Car B:

`m_A` *
`v_A`+
`m_B` *
`v_B` = (m_A + m_B) *
`v_f`

where:

`m_A` is the mass of Car A

`v_A` is the initial velocity of Car A

`m_B` is the mass of Car B

`v_B` is the initial velocity of Car B

`v_f` is the final velocity of both cars after the collision

We know the following:

`m_A` = 1550 kg

`m_B` = 2100 kg

`v_B` = 0 m/s (Car B was stopped at the time of the collision)

`v_f`= 6.64 m/s (the final velocity of both cars after the collision)

We can solve for
`v_A`, the initial velocity of Car A:

`v_A` =
`(m_A + m_B)` *
`v_f - m_B`*
`v_B / m_A`

`v_A` = (1550 kg + 2100 kg) * 6.64 m/s - 2100 kg * 0 m/s / 1550 kg

`v_A` = 14.25 m/s

Converting
`v_A` to mph:

`v_A` = 14.25 m/s * 2.2369 mph/m/s

`v_A` = 31.7 mph

Based on the conservation of momentum, we can determine that Car A was traveling at a speed of 31.7 mph before the collision. The speed limit is 35 mph, so Car A was not speeding at the time of the collision.

Answer 2

option (2) is correct .

Step-by-step explanation:

For Doppler effect in radar the formula is as follows

Δf = f₀ x 2v /c

Δf is change in frequency in reflected wave , f₀ is original frequency , v is velocity of source and c is velocity of right .

Δf = 2460 Hz , f₀ = 1.0525 x 10¹⁰ Hz , v = ? c is velocity of light .

2460 = 1.0525 x 10¹⁰ x 2 v / 3 x 10⁸

2460 = 105.25 x 2 v / 3

v = 2460 x 3 / (105.25 x 2 )

v = 35 .06 m /s .

(b)

Since the observed frequency is less , the source is moving away from the observer .

option (2) is correct .