Math CentralQuandaries & Queries


Question from James:
if a 5 ounce object traveling at 60 mph at 100 feet above the ground, how far will it travel forward before hitting the ground.


  1. The mass is irrelevant if you are ignoring air resistance [remember the (apocryphal) story of Galileo and the Leaning Tower?]
    If you are not ignoring air resistance, you need information about the
    shape and density of the body that you haven't been given. [Five ounces of lead will act quite differently from five ounces of cottonwool, and a skydiver with a folded parachute differently from one who has pulled the ripcord.]

  2. You haven't stated what direction it's travelling in initially: can we presume horizontally?

    Now, find out how long in seconds it takes to hit the ground; use the formula d = 1/2 g t2 where g = -32 ft per second squared. The horizontal motion will not affect this.

    Then convert 60mph to feet per second and find out how far it travels forward in the time you found above. The vertical motion will not affect this.

Good Hunting!

Jim wrote back

I just wanted to let you know that I fly radio controlled airplanes as my hobby. While recently flying, lost a motor, mid air.

I am trying to locate this motor in the field where I was flying. That is why I need an answer to my question.

Thanks a lot!


OK, with a motor we can probably ignore air resistance to *some* extent.

100 = 16 t2 => t = 2.5 seconds

60 mph is 88 feet per second

Typing 60 mph in feet per second yields 60 mph = 88 feet per second.

so in vacuum it would travel 220 feet.

Air resistance will cause it to fall short of this point but
I can't say by how much.


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