1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Kinematics involving an airplane

  1. May 28, 2016 #1
    1. The problem statement, all variables and given/known data
    A bomb is dropped from an airplane at an attitude of 14400 ft. The plane is moving at 600 miles per hour. How far will the bomb move horizontally after it is released from the plane?

    2. Relevant equations
    I use the formula involving the distance traveled by an object with no air resistance and the Pythagorean theorem.

    (1) d= vt - 0.5gt^2
    (2) a^2 + b^2 = c^2

    3. The attempt at a solution
    1 mile = 5280 ft
    g = 32 ft/sec^2
    the plane's speed = 600 miles per hours = 880 ft per sec

    Assuming that the airplane has no vertical velocity, I let v = 0 in the first equation above.
    Then, -14400 = -(0.5)(32)(t^2)
    Solving for t gives t = 30 sec.

    Next, the diagonal distance from the point at which the bomb is on the ground to the plane is
    (880)(32)=28160 miles.

    To find the horizontal distance traveled by the bomb, I use the Pythagorean formula

    horizontal distance = square root of (28160^2 - 14400^2) = 24200 ft = 4.58 miles

    My answer is wrong. The answer key says 5 miles. What did I do wrong?
    Please explain it. Thank you very much
  2. jcsd
  3. May 28, 2016 #2
    Your work for the first part is correct the time is 29.9 seconds to reach the ground. For the second part what you did is incorrect the path is a parabola so the diagonal distance is not what you wrote there.

    To find the horizontal displacement use d = vxit + 1/2 ax t2
    You know the initial velocity in the x direction, and you know that the acceleration is zero since the only force acting on the body is the downward weight
  4. May 28, 2016 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Always pay attention to the units you are using.

    880 is in feet/second.
    It's not clear if 32 represents g in ft/s2 or if it is supposed to be the time of fall of 30 seconds.

    In any event, the result does not come out in units of miles. 28160 miles is larger than the diameter of the earth!
  5. May 28, 2016 #4
    How did you get the diagonal distance by multiplying the horizontal speed with the gravitational attraction?

    Anyway, the key thing here is that the horizontal distance travelled by the bomb only depends on the horizontal component of it's velocity. The horizontal distance is unaffected by the vertical component. Thus when the bomb leaves the plane it has a horizontal velocity of 880 ft/sec and the time for the journey as you found out was 30 sec. Therefore horizontal distance travelled is [itex] 880 \frac{ft}{s} * 30 s = 26400 ft = 5 miles [/itex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted