Motion in Two and Three Dimensions and airplane

In summary, the conversation discusses the calculation of the distance at which a heavy bomb should be released from an airplane in order to hit a target, given the altitude, speed, and other variables. The correct answer is 417m, which was found through using various equations and converting units correctly. Despite some initial mistakes, the individuals were able to come to the correct solution.
  • #1
patelkey
16
0
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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  • #2
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
No I actually got that answer through a different method, however, the correct answer is 417 m.
 
  • #4
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
150km/h=41.6666667m/s
==>
d=(41.6666667m/s)*sqrt(2*500m/(9.8m/s^2))=417m

Thar's your 417m.
 
  • #6
Wow your right
I also converted units wrong
this problem was really annoying,
thanks for the help!
 

Related to Motion in Two and Three Dimensions and airplane

1. What is the difference between motion in two and three dimensions?

Motion in two dimensions refers to movement along a flat surface, such as a plane or coordinate system. This type of motion involves two perpendicular axes, typically labeled as x and y. On the other hand, motion in three dimensions involves movement in three perpendicular directions, typically labeled as x, y, and z. This type of motion is more complex and occurs in three-dimensional objects, such as airplanes.

2. How does an airplane move in two dimensions?

An airplane moves in two dimensions by adjusting the angle of its wings and using its engines to create lift and thrust. By changing the angle of its wings, the airplane can move up and down (pitch) and side to side (roll). The engines provide the necessary thrust to move the airplane forward (yaw).

3. What factors affect an airplane's motion in three dimensions?

Several factors affect an airplane's motion in three dimensions, including air resistance, gravity, and the forces applied by the airplane's control surfaces (such as the rudder, elevators, and ailerons). These forces must be carefully balanced and controlled by the pilot to achieve stable and controlled flight.

4. How is the velocity of an airplane measured in two and three dimensions?

In two dimensions, the velocity of an airplane can be measured by its speed (distance traveled over time) and direction (angle of its movement). In three dimensions, the velocity is measured by its speed in each of the three axes (x, y, and z) and the direction of its movement in each of these axes.

5. How do airplanes maintain equilibrium in three dimensions?

Airplanes maintain equilibrium in three dimensions by balancing the forces acting on it. This is achieved through careful control of the airplane's control surfaces and by adjusting the thrust and lift generated by its engines and wings. If these forces are not balanced, the airplane may experience unstable flight or even enter a state of aerodynamic stall.

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