Amissile is moving 1350 m/s at a 25 degree angle. it needs to hit a target 23,500 m away in a 55 degree direction in 10.20 seconds. what is the direction of its final velocity?

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Explanation:

We know that the initial speed is:

1350 m/s at a 25 degree angle

And the final position after 10.20 sec is:

23,500 m away in a 55 degree direction

In this problem we have:

Final position in x:

Where is the initial velocity in x

So:

We solve for

X component of velocity

Where is the acceleration in the direction x

And

Therefore:

Final position in y:

Where is the initial velocity in y

So:

We solve for

Y component of velocity

Where is the acceleration in the direction y

And

Therefore:

Note then that the final velocity V is a two component vector

The magnitude of the final speed is:

And the angle that forms with the x axis is:

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