A car of mass 2900 kg collides with a truck of mass 4800 kg, and just after the collision the car and truck slide along, stuck together. The car's velocity just before the collision was < 34, 0, 0 > m/s, and the truck's velocity just before the collision was < -18, 0, 28 > m/s
(a) What is the velocity of the stuck-together car and truck just after the collision?
just conserve momentum:
2900<34,0,0> + 4800<-18,0,28> = (2900+4800)v
<98600,0,0>+<-86400,0,134400> = 7700v
<12200,0,134400> = 7700v
v = <1.58,0,17.45>
To find the velocity of the car and truck just after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity.
Let's start by calculating the total momentum before the collision:
Momentum of the car = mass of the car × velocity of the car
= 2900 kg × <34, 0, 0> m/s
= <98600, 0, 0> kg·m/s
Momentum of the truck = mass of the truck × velocity of the truck
= 4800 kg × <-18, 0, 28> m/s
= <-86400, 0, 134400> kg·m/s
Now, let's add the momenta of the car and truck to find the total momentum before the collision:
Total momentum before collision = Momentum of the car + Momentum of the truck
= <98600, 0, 0> kg·m/s + <-86400, 0, 134400> kg·m/s
= <12200, 0, 134400> kg·m/s
Since the car and truck slide along stuck together after the collision, their combined mass is the sum of their individual masses:
Combined mass = mass of the car + mass of the truck
= 2900 kg + 4800 kg
= 7700 kg
Finally, we can find the velocity of the stuck-together car and truck just after the collision by dividing the total momentum before the collision by the combined mass:
Velocity of stuck-together car and truck = Total momentum before collision / Combined mass
= <12200, 0, 134400> kg·m/s / 7700 kg
= <1.5844, 0, 17.4545> m/s
Therefore, the velocity of the stuck-together car and truck just after the collision is approximately <1.5844, 0, 17.4545> m/s.
To find the velocity of the stuck-together car and truck just after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity.
Given:
Mass of the car (m1) = 2900 kg
Mass of the truck (m2) = 4800 kg
Velocity of the car just before the collision (v1) = < 34, 0, 0 > m/s
Velocity of the truck just before the collision (v2) = < -18, 0, 28 > m/s
Now, let's calculate the total momentum before the collision:
Total momentum before the collision = (m1 * v1) + (m2 * v2)
Plugging in the values:
Total momentum before the collision = (2900 kg * <34, 0, 0> m/s) + (4800 kg * <-18, 0, 28> m/s)
Now, we can calculate the momentum of the stuck-together car and truck just after the collision. Since they slide along together, their masses combine:
Total mass after the collision = m1 + m2
Plugging in the values:
Total mass after the collision = 2900 kg + 4800 kg
Finally, the momentum after the collision is given by:
Total momentum after the collision = (total mass after the collision) * (velocity after the collision)
Let's calculate the velocity after the collision by rearranging the equation:
Velocity after the collision = Total momentum after the collision / Total mass after the collision
Plugging in the calculated values, we can find the velocity after the collision.