# Motion in Two and Three Dimensions and airplane

1. Oct 21, 2009

### patelkey

The airplane shown is in level ﬂight at an altitude of 0.50 km and a speed
of 150 km/h. At what distance d should it release a heavy bomb to hit the
target X?

-I tried using x-x0=(v0)(cos(theta))t; and then solving for t with another equation but that does not give me the correct answer when I solve for x. Any suggestions?

2. Oct 21, 2009

### elliotr

Assume it isn't moving for a second. h=500m=0.5*g*t^2 => t=sqrt(2*500m/(10m/s^2)). So it will be in the air for this long. Now assume it is moving along the x-axis for this period of time, t. The distance it will travel will simply be t*(horizontal speed). So if it is moving at 2.5km/s, the distance d will be (2.5km/s)*sqrt(2*500m/(10m/s^2)).

Does this help?

3. Oct 21, 2009

### patelkey

No I actually got that answer through a different method, however, the correct answer is 417 m.

4. Oct 21, 2009

### elliotr

I'm getting the correct answer to be 414.1m, and that is using what I explained earlier. Except I converted units wrong because I'm tired. :) 150km/h = 41m/s

d=(41m/s)*sqrt(2*500m/(9.8m/s^2))=414m. This is definitely correct.

5. Oct 21, 2009

### elliotr

150km/h=41.6666667m/s
==>
d=(41.6666667m/s)*sqrt(2*500m/(9.8m/s^2))=417m

Thar's your 417m.

6. Oct 21, 2009

### patelkey

Wow your right
I also converted units wrong
this problem was really annoying,
thanks for the help!

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