Math 304
A supplementary problem for Section 6.6
According to Newton’s second law of motion, a body near the earth’s surface falls vertically
downward according to
s=s0+v0t+.5gt2
where sis vertical displacement downward relative to some fixed point, s0is initial displacement
at time t= 0,v0is initial velocity at time t= 0,gis acceleration of gravity at earth’s surface.
Suppose a lab experiment is performed to evaluate gusing this equation. A weight is released
with unknown initial displacement and velocity and at certain times the distances fallen from
some fixed reference point are measured. In particular, suppose that at times t=.1, .2, .3, .4, .5
seconds it is found that the weight has fallen s=−.18, .31,1.03,2.48,3.73 feet, respectively,
from the reference point. Find an approximate value of gusing these data.
Answer: gis approx. 32.2ft/s2.
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