A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and stick together.What is their speed after the collision?
A)13.8 m/s
B)15.3 m/s
C)18.8 m/s
D)19.0 m/s
E)21.0 m/s

Question

Quizplus · Accepted Answer

The speed after the collision can be found using the conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. The momentum of each vehicle before the collision is given by $p = mv$, where $m$ is the mass and $v$ is the velocity. The total momentum in the x-direction (west-east) before the collision is $p_{x,car} = (1000\,kg)(-17.0\,m/s)$ (negative because it's west), and in the y-direction (north-south), it's $p_{y,truck} = (1500\,kg)(20.0\,m/s)$. After the collision, the car and truck move together with a combined mass of $2500\,kg$ and a velocity $v$ at an angle $\theta$ to the north. The magnitude of the velocity can be found using the Pythagorean theorem, $v = \sqrt{v_x^2 + v_y^2}$, where $v_x$ and $v_y$ are the velocities in the x and y directions, respectively. Substituting the values, $v = \sqrt{(-17.0)^2 + 20.0^2} = 13.8\,m/s$.

A 1000-Kg Car Is Travelling West at 17