Solve 3D Projectile Motion Homework

[tornzaer]

Homework Statement

A projectile of mass 1 kg is launched from ground level toward the east at 200 metres per second, at an angle of pi/6 to the horizontal. A northerly win applies a force of 2 Newtons to the projectile. Find the location of the projectile and its speed at impact.

Homework Equations

I have to use calculus and derivatives.

The Attempt at a Solution

Since the mass is 1 kg, the force is equal to the acceleration (F= m a). If east is X-axis, then north is Y-axis and gravity acts in the Z-axis. So, a=(0 i , 2 j , -9.81 k).
This is where I'm stuck. I don't know how to proceed.

Please help. Thanks.

 

[tornzaer]

Anyone? I need some help because this is due tomorrow morning.

 

[mgb_phys]

I have to use calculus and derivatives.

no you don't

Just like how you consider the vertical and horizontal components separately to calculate the normal flight of the object. Here you just have to then consider the x and Y components of the motion separately.
resolve the forces into x and Y and it's pretty striaght forward.

ps. by posting in your own question it marks it as answered and so people ignore it!

 

[tornzaer]

How can I make it in terms of x and y components when I have a z component as well?

 

[mgb_phys]

You do that separatly.
Ignore the X and Y, just do the normal trajectory stuff to get the flight time

Then use the force north to work out the curve in XY -
edit, sorry you do need calculus for this, I misread it as a constant accelration, not a constant force

ps. Be careful about which direction a northerly wind is!

 

[zgozvrm]

I came up with the following answers (rounded to 2 decimal places), can anyone verify?

The projectile lands 3559.25 m away from its launch point at a heading of 353.28 degrees and a speed of 204.12 m/s