If a 7kg object is thrown straight upwards at a speed of 10m/s(meters per second)

To what height will it rise? note: gravitational constant = -9.8m/s

When the 7kg object is released (or any object of mass m, for that matter), it has kinetic energy Ek=.5mv², where v is its velocity of 10 m/s. When the object attains its maximum height, it's velocity (and therefore its kinetic energy) will be zero, but what it has instead is potential energy Ep=mgh, where h is its height above a reference point. Since energy is conserved between these two states, we know that

Ek=Ep
.5mv²=mgh

Solving for h,

h=v²/2g
h=10²/(2*9.8)
h=5.1 m

So, regardless of its mass, any object thrown upward at a rate of 10 m/s will rise 5.1 m above the height at which it was released. This calculation ignores losses to wind resistance etc., but these are negligible for this scenario.

Posted by Bryan on 2003-04-01 09:18:12