At an intersection a car of mass 900kg traveling east collides with a pick up truck of mass 1800kg that is traveling North. Two vehicles stick together as a result of the collision, and after collision, the wreckage is sliding at 16m/sec in the direction 24 degrees East of North. Calculate the speed of each vehicle before collision
To calculate the speed of each vehicle before the collision, we need to use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. In this case, we have two objects: the car and the pickup truck.
Let's denote the speed of the car before the collision as V1, and the speed of the pickup truck before the collision as V2. We also know the final velocity of the wreckage after the collision, which we will denote as Vf.
Since the wreckage is sliding at 16 m/s in the direction 24 degrees East of North, we can break down this velocity into its components. The horizontal component would be Vf * cos(24°), and the vertical component would be Vf * sin(24°).
Since the two vehicles stick together and move as one after the collision, we can equate their momentum before and after the collision:
(mass of car * V1) + (mass of pickup truck * V2) = (total mass after collision * Vf)
Now let's substitute the given values into the equation:
(900 kg * V1) + (1800 kg * V2) = (2700 kg * 16 m/s)
Simplifying the equation, we have:
900V1 + 1800V2 = 43200
We need one more equation to solve for V1 and V2. Since the wreckage is sliding at an angle of 24 degrees East of North, we can use trigonometry to find the relationship between the horizontal and vertical components of the final velocity:
Vf * cos(24°) = V1
Vf * sin(24°) = V2
Now we have a system of two equations:
900V1 + 1800V2 = 43200
Vf * cos(24°) = V1
Vf * sin(24°) = V2
Let's substitute the values of V1 and V2 in terms of Vf:
900(Vf * cos(24°)) + 1800(Vf * sin(24°)) = 43200
Simplifying further:
900Vf * cos(24°) + 1800Vf * sin(24°) = 43200
We can now solve this equation to find the value of Vf, which is the final velocity of the wreckage after the collision.
Once we find Vf, we can substitute it back into the equations for V1 and V2 to calculate their speeds before the collision.
Note: The angles mentioned are given in degrees. When using a scientific calculator or programming code, make sure to convert them to radians by multiplying them by π/180.