Finding the Landing Point of a Missile Dropped from a Plane at an Angle

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Homework Help Overview

The problem involves a missile being dropped from a plane traveling horizontally at 200 m/s. The missile has a constant acceleration of 7 m/s² at an angle of 10 degrees below the horizontal, and the plane is at a height of 1250 m when the missile is released. The objective is to determine how far the missile will land in the horizontal direction from the point of release.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss breaking down the acceleration into x and y components using trigonometric functions. There are attempts to calculate the time until the missile hits the ground and to determine the horizontal distance traveled based on various calculations.

Discussion Status

Some participants have provided feedback on the calculations, indicating that the approach to finding the time of flight and the use of kinematic equations is on the right track. However, there are points of confusion regarding the initial velocity of the missile and how it affects the calculations for horizontal distance.

Contextual Notes

There is uncertainty regarding the correct application of kinematic equations and the handling of initial velocities in the context of the problem. Participants are working within the constraints of the problem statement and exploring different interpretations of the setup.

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Homework Statement


a plane, traveling at 200 m/s in the X direction, drops a missile which has a constant acceleration of 7 m/s^2 at an angle 10 degrees below horizontal. If the plane is 1250 m high when it fires, how far (in the x direction) from where it was fired will the missile come down?

Homework Equations


?

The Attempt at a Solution


I have absolutely no idea how to start this problem... could I possibly break the 7m/s^2 into y and x components using cosine, sine and the angle of 350 (10 degrees below the horizontal)?
 
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Sounds like a start.
 
Bystander said:
Sounds like a start.
okay...well how can I possibly keep going after that?
 
DeathEater said:
okay...well how can I possibly keep going after that?
How about if you go that far and see if anything occurs to you.
 
phinds said:
How about if you go that far and see if anything occurs to you.
okay so I'm very much so struggling with this problem, but I tried to solve for the time when the missile will hit the ground

Δy=Voy(t) + ½ ay(t)2 → -1250= 0 (t) +½ (-1.2155) (t)2→ t= 45.35 seconds

is that correct so far?
 
Looks about right --- haven't got my calculator to check for dotting "i's" and crossing of "t's" as far as sin(10°), but definitely the correct ballpark and handling of the numbers. Please continue.
 
Bystander said:
Looks about right --- haven't got my calculator to check for dotting "i's" and crossing of "t's" as far as sin(10°), but definitely the correct ballpark and handling of the numbers. Please continue.
after that, I plugged t into the equation Vfx= Vox +ax(t) → Vfx= 200+(6.894)(45.35) → and got 512.643 m/s for Vfx. I then multiplied the final velocity by the time (45.35 seconds) to get the Δx, which is 23248.3555 m . Is that correct?
 
That non-zero initial velocity tripped you up. How far does the missile travel if the initial velocity is zero? You did fine with the y-component.
 
so should it just be (6.894)*(45.35) then? With that I get an initial of 312.643 and then multiplied by time I get 14178.3555 m
 
  • #10
You used "d = (1/2)at2" for the y-component. I told you that was correct.
 

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