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

[DeathEater]

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

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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)?

 

[Bystander]

Sounds like a start.

 

[DeathEater]

Sounds like a start.

okay...well how can I possibly keep going after that?

 

[phinds]

okay...well how can I possibly keep going after that?

How about if you go that far and see if anything occurs to you.

 

[DeathEater]

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?

 

[Bystander]

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.

 

[DeathEater]

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?

 

[Bystander]

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.

 

[DeathEater]

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

 

[Bystander]

You used "d = (1/2)at²" for the y-component. I told you that was correct.