Motion in Two and Three Dimensions and airplane

AI Thread Summary
The discussion focuses on calculating the distance from which an airplane should release a bomb to hit a target while flying at an altitude of 0.50 km and a speed of 150 km/h. Participants explore the use of kinematic equations to determine the time of fall and the horizontal distance traveled. The correct answer for the release distance is established as 417 meters, with calculations involving unit conversions and the gravitational constant. Participants acknowledge initial errors in unit conversion and appreciate the collaborative problem-solving process. The conversation highlights the importance of accurate calculations in physics problems involving motion in two and three dimensions.
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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?
 
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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?
 
No I actually got that answer through a different method, however, the correct answer is 417 m.
 
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.
 
150km/h=41.6666667m/s
==>
d=(41.6666667m/s)*sqrt(2*500m/(9.8m/s^2))=417m

Thar's your 417m.
 
Wow your right
I also converted units wrong
this problem was really annoying,
thanks for the help!
 

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