At the intersection of Texas Avenue and University Drive, a...

At the intersection of Texas Avenue and University Drive, a yellow subcompact car with mass 950 kg traveling east on University collides with a red pickup truck with mass 1900 kg that is traveling north on Texas and has run a red light ($\textbf{Fig. E8.41}$). The two vehicles stick together as a result of the collision, and the wreckage slides at 16.0 m/s in the direction 24.0$^\circ$ east of north. Calculate the speed of each vehicle before the collision. The collision occurs during a heavy rainstorm; ignore friction forces between the vehicles and the wet road. Figure E8.41 (CANT COPY FIGURE)

Key Concepts

Simultaneous Equations

Solving problems involving momentum conservation in two dimensions often requires setting up and solving a system of equations. Each equation corresponds to the conservation of momentum in one direction, and solving these equations simultaneously enables one to find the unknown quantities such as the initial speeds of the colliding objects.

Vector Decomposition

Vector decomposition involves breaking a vector into its orthogonal components, typically along the x-axis and y-axis. This technique is essential in collision problems that occur in two dimensions, as it allows one to separately analyze and balance the momentum in each independent direction.

Conservation of Linear Momentum

In any collision within an isolated system, the total momentum is conserved even though kinetic energy may not be. This means that the vector sum of the momenta before the collision must equal the vector sum after the collision, making it fundamental for analyzing collisions in both one and two dimensions.

Inelastic Collisions

An inelastic collision is one in which the colliding bodies stick together after impact, resulting in a common final velocity. In this situation, while momentum is conserved, some of the kinetic energy is lost as thermal energy, sound, or deformation, and this aspect distinguishes inelastic collisions from elastic ones.

Transcript

00:01 So the question right here is asking us to find the initial velocities of a car and a pickup truck when they crash together.

00:08 And after they crash, they're moving at 16 meters per second in the direction of 24 degrees east of north.

00:16 So by reading the question, we can tell that this is an inelastic equation question.

00:23 And the inelastic equation goes a little bit like this.

00:26 M1 multiplied by v1 equals m1 plus m2 all multiplied by the final velocity.

00:38 So we can create, firstly let's draw the diagram.

00:42 So this is the mass of the car plus the mass of the truck.

00:50 And now it's moving at 16 meters per second and the angle of 24 degrees east of north.

01:04 So me personally, i prefer to work with this angle here, which would be north of east, and in order to get that angle, you can just do 90 minus 24, and that will give you 66.

01:19 So instead of 24 east per north, we can use 66 north of east.

01:29 So we know our two givens, which is the mass of the car, and the mass of the car is 950 kilograms.

01:38 And we also know the mass of the truck, which is 1900 kilograms.

01:44 So now this is just a matter of isolating the equation and trying to find the first initial velocity of each car.

01:54 But because they're moving in a diagonal direction, we need to split this question into two components.

02:05 So firstly, let's find the velocity in the x direction...

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