# Q & A: Throwing Farthest

Q:
THE FURTHEST BALL if i wish to throw a ball the furthest away from a flat roof of a tall building,at which derees should i do that? a]0 degrees,or straight out of the building. b]upwards at 45 degrees. c]downwards at 45 degrees. d]straight up at 90 degrees.
- wanting (age 12)
singapore
A:
Ignoring air resistance, the horizontal distance a thrown ball will travel before hitting the ground is just the product of two simple quantities:
i) The time the ball spends in the air.
ii) The horizontal component of the balls velocity.

If you were standing on level ground, you would want to throw the ball upwards at a 45 degree angle to make this product a maximum.

If you are standing on a tall building (where "tall" means that its much much higher than you can throw), then the time that the ball spends in the air is almost entirely determined by the height of the building. In other words, throwing it upward or downward will not change the time the ball spends in the air by a sizeable fraction. Since you cant change the time spent in the air by much, the best thing you can do to make the ball go farther is give it the biggest possible horizontal velocity when you throw it. This is done by throwing it horizontally, which is your answer [a].

If you worked this out exactly, you would find that you should throw it just a tiny bit above horizontal, where the exact amount would depend on the height of the building, the air resistance etc. This would not change the answer to your question, though, since the exact angle would be much closer to 0 degrees than any of the other answers you list.

Mats

(published on 10/22/2007)