speedboat a negotiates a curve whose radius is 120m. speedboat b negotiates a curve whose radius is 240m. each boat experiences the same centripetal acceleration. what is the ration va/vb of the speeds of the boats? i do not need the answer necessarily, i need to understand how to get to the answer!~
2006-09-29 09:19:54 · 2 answers · asked by Amanda R 2 in Science & Mathematics ➔ Physics
let aa=angular acceleration of boat a
ab=angular acceleration of boat b
va=velocity of boat a
vb=velocity of boat b
ra=radius of boat a
rb=radius of boat b
the formulas are as followed:
aa=va^2/ra
ab=vb^2/rb
since angular acceleration is constant for these two,
aa=ab
so substitute the formulas for both a's and we have:
va^2/ra=vb^2/rb
insert values for ra=120m and rb=240m
va^2/120m=vb^2/240m
multiply equation by 120m
va^2=(120m*vb^2)/240m
divide equation by vb^2
va^2/vb^2=120m/240m
m's cancel out and 120/240 simplifies to 1/2
va^2/vb^2=1/2
take saquare root (sqrrt) of equation
va/vb=1/sqrrt2
2006-09-29 10:54:51 · answer #1 · answered by D 1 · 1⤊ 0⤋
The "how to" part is straightforward algebra. Centripetal acceleration = v^2/r. Set up the equation of the situation:
va^2/r = vb^2/(2r)
Then rearrange to get va/vb:
va^2/vb^2 = r/(2r)
(va/vb)^2 = 1/2
va/vb = SQRT(1/2)
2006-10-02 12:21:21 · answer #2 · answered by kirchwey 7 · 0⤊ 0⤋