# Glancing Collisions

ScoutFCM
I'm stuck, for the past 30 minutes. Anyone care to give a struggling student a hand? Any help would be appreciated due to that fact that I don't understand the material. I have notes, yet I have one of those teachers who talk, but don't teach. I don't know. Thanks to anyone who can help me out.

1.) An 8.00g bullet is fired into a 250g block that is initially at rest at the edge of a table of height 1.00m. The bullet remains in the block and after the impact the block lands 2.00m from the bottom of the table. Determine the initial speed of the bullet.

2.) A 1200kg car traveling initially with a speed of 25m/s in an eaterly direction crashes into the rear end of a 9000kg truck moving in the same direction at 20m/s. The veolcity of the car right after the collision is 18m/s to the east. What is the velocity of the truck right after the collision? How much mechanical enegry is lost in the collision? Account for this loss in energy.

3.) Two automobiles of equal mass approach an intesection. One vehicle is traveling with velocity 13m/s toward the east and the other is traveling north with speed V2i. Neither driver sees each the other. The vehicles collide in the intersection and stick together, leaving parallel ski marks at an angle of 55 degrees north of east. The speed limit for both roads is 35mi/hr and the driver of the northward-moving vehicle claims he was within the speed limit when the collision occurred. Is he telling the truth?

## Answers and Replies

Gold Member
1. Assume the table is frictionless so that the velocity it gets after the collision is the same as the velocity it has as it leaves the table. The first thing you should do is find what this velocity is: you know how far away from the table it landed and how high it started off, so just use kinematics to find what the initial (x) velocity must have been. Then use the conservation of momentum. This is an inelastic collision and the block starts at rest, so you can simply write mv = (m+M)V, where m is the bullet mass, M is the block mass, v is the unknown bullet velocity, and V is the velocity you just found from kinematics.

2. Use the conservation of momentum. If you write some work out for this one, I (or someone else) will try to give more specific help. You can calculate the kinetic energy before and after the collision to find how much was lost. Where do you think the energy may have been lost to?

3. Again, conservation of momentum. Remember that momentum is a vector quantity, so that when you have a 2-dimensional problem like this one, you will get 2 equations (assuming you resolve things into components). You know the orientation of the post-collision momentum along with the fact that the vehicles stick together (effectively become one mass) after the collision. It will be easier on both of us if you write out your initial thoughts and equations on this problem. Once you have solved for the unknown initial velocity of the north-bound driver, you can convert it to the proper units and determine if he was above or below the speed limit.

ScoutFCM
Geez, you should be my teacher. Your explanation in 6 lines taught me more than my teacher did in 3 class periods. Haha. Off to doing my work.....