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Name: Robert
Status: other
Age: 40s
Location: N/A
Country: N/A
Date: Monday, December 11, 2002


Question:
Hello, I have searched your site for an answer to my question with no luck, so here goes....

Trajectory question : Please describe the trajectory of a projectile fired from an airplane under these two circumstances, 1) the projectile is fired FORWARD, in the direction of travel, and 2) the projectile is fired REARWARD, directly opposite the direction of travel. For the sake of argument, let us say the speed of the aircraft is 1000 feet per second and the speed of the projectile is also 1000 fps.

I am having difficulty understanding the correlation between the aircraft, the projectile, with ground speed vs airspeed further confusing the issue. Does the projectile when fired forward, fly away from the plane at a rate of 1000 fps.,(with a total rate of travel at 2000 fps. (airspeed...ground speed?)? Conversely when fired away from the direction of travel, does the projectile just "stay" with the plane until gravity pulls it to earth?


Replies:
Robert,

Let us assume that air speed and ground speed are the same for the aircraft (i.e., the air is not moving relative to the ground). Since the projectile is fired from the frame of reference of the aircraft the projectile velocities are with respect to [wrt] the aircraft speed. The projectile's ground speed is the aircraft ground speed plus the speed of the projectile wrt the aircraft. When the projectile is fired forward the projectile speed is positive when it is fired to the rear its speed is negative.

Greg Bradburn


You have the forward case right; the projectile has a ground speed of 2000 fps. It keeps moving at 2000 fps horizontally but its vertical speed (toward the ground) increases as would any other dropped object. (I am neglecting drag.) The reverse case is the same math: the ground speed of the projectile is zero; it just drops straight to the ground. In both cases the horizontal speed of the projectile with respect to the plane is 1000 fps.

Tim Mooney


Robert,

The plane and the projectile are already moving forward at 1000 fps. The launch speed is how much the velocity of the projectile changes during the launch. Let's look at everything as seen from the ground.

When fired forward, the velocity increases from 1000 fps to 2000 fps. Now the projectile is moving forward much faster than the plane. Assuming air resistance does not do anything extreme, the projectile will continue with this horizontal velocity because gravity cannot change it. Now that the projectile is no longer supported by the plane's floor, it begins to drop. This is the effect of gravity. The vertical velocity increases the same as for a dropped ball.

When the projectile is fired backward, the velocity decreases from 1000 fps to 0 fps. Now the projectile is not moving. The plane continues forward at 1000 fps. The projectile never gets any horizontal velocity because gravity can't change it. Vertical velocity does change, just as for the forward-fired projectile. The projectile drops straight down.

In both cases, the difference in velocities between the projectile and the plane is 1000 fps. To someone on the plane, the forward-fired projectile looks like it moves at 1000 fps forward. The backward-fired projectile looks like it moves at 1000 fps backward. You can only say one is more correct than the other if you know for a fact which observer truly has zero velocity. This is something nobody knows. Many people swear that the surface of the Earth does not move. The Earth rotates. At the equator, this requires a speed of about 25,000 miles per day: more than 1,000 miles per hour. Just be sure all measurements are in the same reference frame before applying any laws of physics.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College



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