Finding the angle of release from a moving plane that drops an object X distance away

In summary: So it's just a matter of finding the angle from the vertical to the sight and then multiplying that by the range.
  • #1
exi
85
0

Homework Statement



A plane flies horizontally @ 299 m/s relative to ground.
Altitude: 3450m, level terrain; neglect air resistance.

1: How far from the point vertically under the point of release does the object land (in meters)?

2: At what angle must the bomb be released so that it hits the target at time of release (in °)?

Homework Equations



t = (sqrt(Voy^2 + 2gh) - Voy) / -g

Range = Vox(t)

The Attempt at a Solution



Using the above, I correctly figured 7933.83 m for the range. It's the angle part that's screwing me.

Now, because the y-component of that object's velocity is zero at release, I was able to answer #1 without breaking anything down. But I have not a clue as to how to find that damn angle.
 
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  • #2
I assume they want the bomb to hit the target nose first. What angle does the velocity make when it hits the target? (Find the velocity components.)
 
  • #3
Doc Al said:
I assume they want the bomb to hit the target nose first. What angle does the velocity make when it hits the target? (Find the velocity components.)

I'm really not sure what I'm doing on this one. Would you mind starting me off a bit?
 
  • #4
exi said:

Homework Statement



A plane flies horizontally @ 299 m/s relative to ground.
Altitude: 3450m, level terrain; neglect air resistance.

1: How far from the point vertically under the point of release does the object land (in meters)?

2: At what angle must the bomb be released so that it hits the target at time of release (in °)?

Homework Equations



t = (sqrt(Voy^2 + 2gh) - Voy) / -g

Range = Vox(t)

The Attempt at a Solution



Using the above, I correctly figured 7933.83 m for the range. It's the angle part that's screwing me.

Now, because the y-component of that object's velocity is zero at release, I was able to answer #1 without breaking anything down. But I have not a clue as to how to find that damn angle.


To me the second question does not make sense. First, the bomb cannot hit the target at the time of release! Second, I have the *feeling* that they mean to ask the angle at which it hits the target, not at which it is released, but I can't tell for sure. Third, if they want an angle of release, they have to give more information (how far the target is when th ebomb is released and more stuff as well). is this the way is exactly phrased??
 
  • #5
nrqed said:
To me the second question does not make sense. First, the bomb cannot hit the target at the time of release! Second, I have the *feeling* that they mean to ask the angle at which it hits the target, not at which it is released, but I can't tell for sure. Third, if they want an angle of release, they have to give more information (how far the target is when th ebomb is released and more stuff as well). is this the way is exactly phrased??

It really is worded like that. "At what angle from the vertical at the point of release must the telescopic bomb sight be set so that the bomb hits the target ... ?" The distance to target is 7933.83 m as figured from the first half of the problem, and the rest of the info is in my post. I'm just having a hard time figuring out what to use and where.
 
  • #6
exi said:
It really is worded like that. "At what angle from the vertical at the point of release must the telescopic bomb sight be set so that the bomb hits the target ... ?" The distance to target is 7933.83 m as figured from the first half of the problem, and the rest of the info is in my post. I'm just having a hard time figuring out what to use and where.

So now you have right triangle composed of a vertical line from the plane to a point directly below on the ground and a horizontal line from that point to the target. The bomb sight points from the plane to the target along the hypotenuse. You know the length of both of these sides and want to find the angle at the corner where the plane is. Sounds like trig to me.
 
Last edited:
  • #7
exi said:
It really is worded like that. "At what angle from the vertical at the point of release must the telescopic bomb sight be set so that the bomb hits the target ... ?" The distance to target is 7933.83 m as figured from the first half of the problem, and the rest of the info is in my post. I'm just having a hard time figuring out what to use and where.

AHHH! It makes a HUGE difefrence to mention the telescopic bomb sight!:rolleyes:
You just have to find the angle at which the target appears from the bomb's point of view when the bomb is released. Dick explained it. It has nothing to do with physics at this point, it's just trigonometry.
 
  • #8
Dick said:
So now you have right triangle composed of a vertical line from the plane to a point directly below on the ground and a horizontal line from that point to the target. The bomb sight points from the plane to the target along the hypotenuse. You know the length of both of these sides and want to find the angle at the corner where the plane is. Sounds like trig to me.

nrqed said:
AHHH! It makes a HUGE difefrence to mention the telescopic bomb sight!:rolleyes:
You just have to find the angle at which the target appears from the bomb's point of view when the bomb is released. Dick explained it. It has nothing to do with physics at this point, it's just trigonometry.

Yeah, sorry for screwing up the original question by trying to over-Cliffs Notes it.

tan^-1 (7933.8264 / 3450) = 66.498° it is.

Thanks. o:)
 

1. What is the angle of release from a moving plane?

The angle of release from a moving plane refers to the angle at which an object is dropped from a plane while it is in motion. It is the angle between the horizontal plane and the direction in which the object is released.

2. How is the angle of release calculated?

The angle of release can be calculated using the distance the object is dropped from the plane, the distance the object travels horizontally, and the acceleration due to gravity. This can be done using trigonometric equations such as the tangent function.

3. What factors affect the angle of release?

The angle of release is affected by the initial speed of the plane, the speed of the object being dropped, the distance the object is dropped from the plane, and the acceleration due to gravity.

4. Why is finding the angle of release important?

Knowing the angle of release is important for accurately predicting the trajectory of the dropped object. This can be useful in various applications, such as in the military for dropping supplies or in sports for determining the optimal angle for a long throw.

5. Can the angle of release be changed once the object is dropped?

No, once the object is dropped from the plane, the angle of release cannot be changed. The object will continue to follow its trajectory based on the initial angle of release and other factors such as air resistance.

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