# What will be the final velocity and direction of two colliding cars?

In summary, the two cars, with masses 800 kg and 1600 kg, respectively, were traveling towards each other at speeds of 36km/h and 54km/h. After the collision, they will move in the same direction with a velocity of 24km/h. This can be determined using the formula $m_1u_1+m_2u_2 = (m_1+m_2)v$, where $m_1$ and $m_2$ are the masses of the cars, $u_1$ and $u_2$ are their initial velocities, and $v$ is the final combined velocity.

## Homework Statement

A car of 800 kg was going towards east with a velocity of 36km/h and an another car of 1600 kg was going towards west with a velocity of 54km/h. After collision, in which direction and with how much velocity will the cars go?

## Homework Equations

$m_1u_1+m_2u_2 = (m_1+m_2)v$

## The Attempt at a Solution

Here, we can take the first cars' mass as 1 and the second car as 2
Then,
$m_1=800kg$
$m_2=1600kg$
$u_1=36km/h$
$=\frac{36*10^3}{60*60}$
$=10m/s$
$u_2=54km/h$
$=\frac{54*10^3}{60*60}$
$=15m/s$

We know,
$m_1u_1+m_2u_2 = (m_1+m_2)v$
$Or, v = \frac{m_1u_1+m_2u_2}{m_1+m_2}$
$= \frac{800*10+1600*15}{800+1600}$
$= 13.33 m/s$ (ans.)

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## Homework Statement

A car of 800 kg was going towards east with a velocity of 36km/h and an another car of 1600 kg was going towards west with a velocity of 54km/h. After collision, in which direction and with how much velocity will the cars go?

## Homework Equations

$m_1u_1+m_2u_2 = (m_1+m_2)v$

## The Attempt at a Solution

Here, we can take the first cars' mass as 1 and the second car as 2
Then,
$m_1=800kg$
$m_2=1600kg$
$u_1=36km/h$
$=\frac{36*10^3}{60*60}$
$=10m/s$
$u_2=54km/h$
$=\frac{54*10^3}{60*60}$
$=15m/s$

We know,
$m_1u_1+m_2u_2 = (m_1+m_2)v$
$Or, v = \frac{m_1u_1+m_2u_2}{m_1+m_2}$
$= \frac{800*10+1600*15}{800+1600}$
$= 13.33 m/s$ (ans.)

[/B]
Can't we use LaTex here?

## Homework Statement

A car of 800 kg was going towards east with a velocity of 36km/h and an another car of 1600 kg was going towards west with a velocity of 54km/h. After collision, in which direction and with how much velocity will the cars go?

## Homework Equations

$$m_1u_1+m_2u_2 = (m_1+m_2)v$$

## The Attempt at a Solution

Here, we can take the first cars' mass as 1 and the second car as 2
Then,
$$m_1=800kg$$
$$m_2=1600kg$$
$$u_1=36km/h$$
$$=\frac{36*10^3}{60*60}$$
$$=10m/s$$
$$u_2=54km/h$$
$$=\frac{54*10^3}{60*60}$$
$$=15m/s$$

We know,
##m_1u_1+m_2u_2=(m_1+m_2)v##
##v = \frac{m_1u_1+m_2u_2}{m_1+m_2}##
$$= \frac{800*10+1600*15}{800+1600}$$ $$= 13.33 m/s$$ (ans.)[/B]
The LaTeX on this site needs double dollar signs front and back. Better, use double hash signs (#) so that it is not forced onto a new line. I've fixed it up in the copy above, but could not get one line to work.
As to your algebra, pay attention to signs. The cars were going in opposite directions.

haruspex said:
The LaTeX on this site needs double dollar signs front and back. Better, use double hash signs (#) so that it is not forced onto a new line. I've fixed it up in the copy above, but could not get one line to work.
As to your algebra, pay attention to signs. The cars were going in opposite directions.
Thanks a lot for your help.
Could you tell me what the answer is?

Is it right?

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haruspex said:
Yes, that is the right answer. You did not need to convert to m/s, though. Since the speeds are given kph you can answer in kph (24).
Thank you. I got it.

Much simpler to use the following formula (for perfectly inelastic collisions):

Δp = μΔv where μ is the reduced mass [m1 * m2 / (m1+m2) ] of the colliding objects and Δv is their relative velocity. Then p1(after) = p1(before) - Δp and you can divide by m1 to obtain the combined velocity.

p1 is the momentum of the heavier vehicle but you could similarly calculate p2(before) - Δp (this answer would be negative) and divide by m2. Same result.

## 1. What causes a collision between two cars?

A collision between two cars is typically caused by one or both drivers not following traffic laws or being distracted. This could include running a red light, speeding, or texting while driving.

## 2. What factors affect the severity of a collision?

The severity of a collision between two cars can be affected by various factors such as the speed of the vehicles, the angle of impact, the weight and size of the vehicles, and the use of safety features like seatbelts and airbags.

## 3. How can collisions between cars be prevented?

Collisions between cars can be prevented by practicing safe driving habits, following traffic laws, avoiding distractions while driving, and maintaining a safe distance from other vehicles. It is also important for drivers to regularly maintain their vehicles to ensure they are in proper working condition.

## 4. What are the potential injuries that can occur in a car collision?

The potential injuries that can occur in a car collision can range from minor bruises and cuts to more serious injuries such as broken bones, whiplash, concussions, and even death. The severity of injuries can depend on the speed and force of the collision, as well as the use of safety features and the overall health and age of those involved.

## 5. How can scientists use data from car collisions to improve safety?

Scientists can use data from car collisions to identify patterns and trends, which can then be used to develop and improve safety measures. This includes designing safer vehicles, creating better road infrastructure, and implementing stricter traffic laws. Studying car collisions can also help scientists understand the effects of different factors, such as speed and impact angle, on the severity of collisions.

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