A car with a mass of 1800 kg is initially travelling with a velocity of 22 m/s [N] when it collides with a truck with a mass of 3200 kg traveling with a velocity of 14 m/s [E]. If the two vehicles become attached during the collision, determine their final velocity.
north momentum before = 1800*22
east momentum before = 3200*14
north momentum after = 5000 Vn
east momentum after = 5000 Ve
so
Vn = 1800*22/5000
Ve = 3200*14/5000
v = sqrt (Vn^2 + Ve^2)
tan angle east of north (compass heading)
= Ve/Vn
I still don't understand.
To determine the final velocity of the car and truck after the collision, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is calculated as p = m * v, where m is the mass and v is the velocity.
Initially, the car has a mass of 1800 kg and a velocity of 22 m/s [N], so its momentum is given by:
Momentum of car = mass of car * velocity of car = 1800 kg * 22 m/s = 39600 kg·m/s [N]
Similarly, the truck has a mass of 3200 kg and a velocity of 14 m/s [E], so its momentum is given by:
Momentum of truck = mass of truck * velocity of truck = 3200 kg * 14 m/s = 44800 kg·m/s [E]
To determine the final velocity, we consider the combined mass of the car and the truck after collision, which is equal to the sum of their individual masses:
Combined mass = mass of car + mass of truck = 1800 kg + 3200 kg = 5000 kg
Now, let's assume the final velocity after the collision is v_final. Since the car and truck are attached after the collision, they move together with the same velocity.
Therefore, using the principle of conservation of momentum, we can write the equation:
Total momentum before collision = Total momentum after collision
(Initial momentum of car) + (Initial momentum of truck) = (Final momentum of combined mass)
(39600 kg·m/s [N]) + (44800 kg·m/s [E]) = (Final velocity of combined mass) * (Combined mass)
Now, we can solve the equation for the final velocity (v_final):
(84400 kg·m/s) = (Final velocity of combined mass) * (5000 kg)
Divide both sides of the equation by 5000 kg:
Final velocity of combined mass = 84400 kg·m/s / 5000 kg = 16.88 m/s
So, the final velocity of the car and truck combined after the collision is approximately 16.88 m/s.