Two cars are approaching a perpendicular intersection without a stop sign. Car 1 has a mass 900 kg and is heading north and car 2 has mass 900 kg and is heading west. The two cars collide at the intersection, and stick together as a result of the collision. The police report stated that after the collision, the two cars were moving in a direction 35o west of north. What is the ratio of the initial speed of car 1 to car 2?

V1/V2 = cos35/sin35 = 1.428

thanKS Henry

Glad I could help.

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Let's assume the initial velocities of car 1 and car 2 are v1 and v2 respectively. The mass of both cars is given as 900 kg.

The momentum of car 1 before the collision is given by p1 = m1 * v1, where m1 is the mass of car 1 and v1 is its initial velocity.

Similarly, the momentum of car 2 before the collision is given by p2 = m2 * v2, where m2 is the mass of car 2 and v2 is its initial velocity.

According to the problem, the two cars stick together and move in a direction 35 degrees west of north after the collision. Let the final velocity of the cars be vf.

Now, the total momentum before the collision is equal to the total momentum after the collision.
p1 + p2 = (m1 + m2) * vf

Substituting the values, we get:
m1 * v1 + m2 * v2 = (m1 + m2) * vf

Now, let's find the ratio of the initial velocity of car 1 to car 2.

Dividing the equation by m2, we get:
(m1/m2) * v1 + v2 = (m1 + m2) * vf / m2

Dividing through by v2, we get:
v1/v2 + 1 = [(m1 + m2) * vf / m2] / v2

Simplifying the equation, we get:
v1/v2 = [(m1 + m2) * vf / m2] / v2 - 1

Now, we can substitute the given values:
v1/v2 = [(900 + 900) * vf / 900] / v2 - 1
v1/v2 = (1800 * vf / 900) / (v2 - 1)

Since vf is the magnitude of the resultant velocity and the direction is 35 degrees west of north, we can use trigonometry to find the value of vf:

vf = vf * sin(35°) (since it's the component perpendicular to the original direction, pointing west)
vf = vf * cos(35°) (since it's the component along the original direction, pointing north)

Now, substituting these values into our equation:
v1/v2 = (1800 * vf * cos(35°) / 900) / (v2 * sin(35°) - 1)

By solving the above equation, you can calculate the ratio of the initial speed of car 1 to car 2.