How can you determine trajectory when something is on, comes from a moving object?

Question

example 1 : If someone is on a school bus travelling at 60 MPH, and then she gets up and walks forward, her speed is 1 MPH, how do you record the speed of the person?

Is her speed 60 mph, 61 mph or should you list it at both velocities : 60 mph + 1 mph.

My thought on this is that speed is relative. Someone on the bus observes her travelling at 1 mph, but someone off the bus observes her at 61 mph (I'm assuming). To account for this you record the speed at 60 +1 mph so that someone looking at the record sees there are two different velocities.

Second example: Someone is travelling in a car and fires a gun that is perfectly perpendicular to their forward direction.

Not accounting for any wind resistance, will the bullet continue to move in the direction of the car?

My guess is that bullets leaving this moving object would form a diagonal (triangle with direction of car, intended direction of bullet and actual direction of bullet. Thoughts from physics students?

Alright, so based on the fact that it appears that I'm right, doesn't this mean that shooters have a much greater challenge than the movies portray when trying to shoot from moving objects (aside from the fact that movies always get their stuff wrong)?

I would think if a bullet is continuing to travel forward and in its own direction that the shooter has 0 chance of hitting a target that's perpendicular to forward motion. (because even if the target were perfectly sited, the bullet will travel ahead of the target)

I would also think that the best way to guarantee accuracy in shooting, then, is to make sure that when you are shooting that you want your bullet to travel as close to the true forward direction of the moving vehicle as possible. Seems to me then that the problem with accuracy will get worse the closer to perpendicular the barrell of the gun will be.....right ?

Answer 1

Since we normally reference things in terms of a still observer on the ground, her speed would be 61mph.

Ignoring resistance and drag, a bullet fired (out the passenger side window lets say) would continue moving in the direction of the car, at the speed the car was moving, as well as moving away from the car at the speed the gun fires, so your mention of a diagonal motion is correct. If you knew the velocities, you could plot vectors and find the angle and velocity.

Answer 2

> Is her speed 60 mph, 61 mph or should you list it at both velocities : 60 mph + 1 mph. My thought on this is that speed is relative.

Right.

> Someone on the bus observes her travelling at 1 mph, but someone off the bus observes her at 61 mph (I'm assuming).

Right.

> To account for this you record the speed at 60 +1 mph so that someone looking at the record sees there are two different velocities.

Right.

> Someone is travelling in a car and fires a gun that is perfectly perpendicular to their forward direction.

> Not accounting for any wind resistance, will the bullet continue to move in the direction of the car?

Yes.

> My guess is that bullets leaving this moving object would form a diagonal (triangle with direction of car, intended direction of bullet and actual direction of bullet.

Right.

Answer 3

The trajectory of the bullet includes the force imparted upon it by the moving car. Thus, it would travel at an angle leaving the car. The angle would be determined by the speed of the car and the speed of the bullet.

Try driving down the road at 30-60 mph and trying to throw something out the window into a trash can. You will see the effect. You have to throw it long before you reach perpendicular to the trash can.

An interesting fact I learned from some war veterans, during WWII, fighter pilots who were approaching a slow bomber would often times need to shoot behind the bomber they were attacking. This was because their forward motion was much greater than the forward motion of the bomber. It was very counter intuitive, but they learned quickly.

Answer 4

Velocity depends on your frame of reference. From the first example, a bystander outside of the bus would see the girl traveling at 61 mph. But, other people on the bus would see her traveling at only 1 mph. So, you must define your frame of reference.

Likewise, for the gun in the car, a bystander would see the bullet travel at normal bullet speed plus the car's speed. But, the shooter would see the bullet travel at only normal bullet speed.

Answer 5

It's relative, Her speed relative to the floor of the bus is 1MPH, her speed relative to the road is 61MPH, as it would be to a stationary onlooker. The bullet moves forward with the speed of the car and upward with the muzzle velocity, the shooter will have to fire slightly behind the target if he has any chance of hitting it.