Boom! (again)
A mortar launches a projectile on a ballistic trajectory. (Assume this takes place in an area of flat ground.)
For purposes of this calculation, assume the gravitational acceleration is exactly 9.8 meters per second squared, downwards.
The projectile is in the air for the smallest possible integral number of seconds that makes its maximum height also an integral number of meters. (The mortar is fired from ground level.)
What is the maximum height (in meters) achieved by the projectile?
The answer is 490.
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1 solution
The maximum height (in meters) is ( 9 . 8 / 8 ) s 2 ,where s is the total flight time in seconds.
9.8/8 = 49/40, so s 2 has to be divisible by 40. This makes s a multiple of 10. 100 is not divisible by 40, but 400 is. So s = 20 seconds. Substituting in, height = 49/40 * 400 = 490 m.