A vehicle travelling 30mph collides head-on with another vehicle travelling 50mph, the force of impact, theoretically, would be the same as a vehicle travelling:
A. 80mph hitting a cement wall
B. 80mph hitting a stopped vehicle
c. 50mph hitting a cement wall
d. 30mph hitting a cement wall
What matters in determining impact damage is the relative velocity and whether of not either car (and the center of mass) is free to move afterwards.
That is only true for case B
Well, that's quite a collision! In this head-on encounter, the force of impact is determined by the change in momentum. So, to find a vehicle traveling with an equal force of impact, we'll need to consider the change in momentum for each scenario.
Let's start with option A. If a vehicle traveling 80mph hits a cement wall, its momentum comes to a screeching halt. The change in momentum is, well, let's say pretty dramatic.
Now, moving on to option B, if a vehicle traveling 80mph hits a stopped vehicle, the change in momentum is less drastic. The moving vehicle transfers some of its momentum to the stationary one, resulting in a smaller impact force compared to hitting a wall.
Option C suggests a vehicle traveling 50mph hitting a cement wall. Here, the change in momentum is certainly considerable, but it's important to note that it's lower than the head-on collision scenario.
Lastly, option D indicates a vehicle traveling 30mph hitting a cement wall. While the change in momentum is still substantial, it's the lowest among all the given scenarios.
So, after considering the various options, the best answer is C. A vehicle traveling 50mph hitting a cement wall would experience a force of impact theoretically equivalent to the head-on collision of the 30mph and 50mph vehicles.
To calculate the force of impact in a head-on collision, we need to consider the concept of momentum. The formula for momentum is:
Momentum = mass × velocity
In a head-on collision, the change in momentum is equal to the force of impact. Since the masses of the vehicles are not mentioned, we assume they are the same.
The momentum before the collision for the first vehicle traveling at 30mph can be calculated as:
Momentum1_before = mass × velocity1 = M × 30
The momentum before the collision for the second vehicle traveling at 50mph can be calculated as:
Momentum2_before = mass × velocity2 = M × 50
After the collision, the first vehicle comes to a stop, and the second vehicle continues moving at a reduced speed.
The momentum after the collision for the first vehicle is:
Momentum1_after = mass × velocity1' = 0 (since it comes to a stop)
The momentum after the collision for the second vehicle is:
Momentum2_after = mass × velocity2'
Now, because the momentum is conserved in a collision, we can set up an equation:
Momentum1_before + Momentum2_before = Momentum1_after + Momentum2_after
M × 30 + M × 50 = 0 + M × velocity2'
Simplifying the equation:
80M = M × velocity2'
We can see that the force of impact, theoretically, would be the same as a vehicle traveling at 80mph hitting a stopped vehicle.
Therefore, the correct answer is B. 80mph hitting a stopped vehicle.
To determine the force of impact in a collision, you need to consider the concept of impulse and momentum. Momentum is defined as the product of an object's mass and velocity, while impulse is the change in momentum caused by a force acting on an object for a certain period of time.
In a head-on collision, the vehicles are moving towards each other with the same force, but opposite direction. When two objects collide, their velocities change, and the principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system.
In this case, the first vehicle is traveling at 30 mph (30 miles per hour), and the second vehicle is traveling at 50 mph (50 miles per hour). Since the force of impact is theoretically the same, we can equate the momentum before and after the collision as follows:
(mass of 1st vehicle × velocity of 1st vehicle) + (mass of 2nd vehicle × velocity of 2nd vehicle) = (mass of 1st vehicle × velocity after collision) + (mass of 2nd vehicle × velocity after collision)
Assuming the masses of the vehicles are the same, we can simplify the equation:
(30 mph × mass) + (50 mph × mass) = 2 × (velocity after collision)
Dividing both sides by 2:
40 mph × mass = velocity after collision
Therefore, the velocity of the vehicles after the collision would be 40 mph.
Now, let's analyze the given options:
A. 80mph hitting a cement wall: This option does not correspond to the calculated velocity after the collision.
B. 80mph hitting a stopped vehicle: This option does not correspond to the calculated velocity after the collision.
C. 50mph hitting a cement wall: This option does correspond to the calculated velocity after the collision, which is 40 mph.
D. 30mph hitting a cement wall: This option does not correspond to the calculated velocity after the collision.
Based on the explanation, the correct option would be C. 50mph hitting a cement wall.