Homework Clinic
Mathematics Clinic => Grade 9 Mathematics => Topic started by: xclash on Oct 4, 2013
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I totally don't understand how to calculate this. Hint: Use potential energy calculation (PEgravitational=mgh) m=mass, g=gravitational field pull (9.8) and h=height, estimated mass, and kinetic energy formula (KE=.5mv^2). I'll try figuring this out again, but it's a problem I've been stuck on! Thank you in advance!
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OK:
At its maximum height, assume the object is not moving up or down. The object posseses
(1) PE = mgh
When it hits the ground, it will have lost all its PE, which will have been converted into KE:
(2) KE = .5*mv^2
The force acting on the object as it falls is
(3) F = ma, where the "a" represents acceleration imparted to m when the force F on it is converted into motion. In the context of the earth's gravity, the "a" is what we symbolize by g:
(4) F = mg, where
g = 9.8 m/s^2 = 9.8 (m/s)/s, (meters per second) per second.
Velocity is meters/second, and acceleration is the rate of change in velocity, or velocity/second.
If you know the acceleration, then you know the velocity after t seconds:
(5) v = gt
Putting all of the above together:
(6) mgh = .5*mv^2 since KE = PE at impact. Substituting for v from (5), we get
(7) mgh = .5 * m * (gt)^2 = .5 * m * g^2 * t^2
Canceling terms common to each side, we get:
h = .5 * g * t^2
Rearranging and solving for t, we get
(8) t = ?(2h / g) <<---ANSWER
Notice that the time is not dependent on the mass.
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