Related rates problems are really interesting. It's pretty cool how you can actually use derivatives to find out something that is related to real life. I know that I am definitely one of those obnoxious, pessimistic people that always complains about math, saying that I'll never use the stuff I learn again in my life, so for me its actually really cool to see how derivatives and rates of change are used in real life situations..
Problem:
Real life example: Every summer I visit my dad in New Jersey, last year when I went to visit my dad my sister, Taryn, flew from New Jersey to the Florida Keys to visit our cousins. If I am on a plane approximately 500 miles west of Newark Airport traveling 250 miles per hour and Taryn is on a plane 50 miles south of Newark airport traveling 210 miles per hour, how fast is the distance between us changing?
a^2+b^2=c^2
a=500
b=50
c=?
500^2+50^2=c^2
250,000 + 2500=252500
c= sq. root of 252500 = 502.49
da/dt=250 mph
db/dt=175 mph
dc/dt=?
d/dt(a^2+b^2)=d/dt c^2
2a*da/dt + 2b*db/dt = 2c*dc/dt
-(2*500*250) + (2*50*175) = (2*502.49*dc/dt)
-250000+17500=1004.98*dc/dt
-232,500/1004.98=dc/dt
-231.34 mph = dc/dt
No comments:
Post a Comment