(Note: The two parts are not related.) (a) Imagine a boat that travels at 6.5 m/
ID: 1418772 • Letter: #
Question
(Note: The two parts are not related.) (a) Imagine a boat that travels at 6.5 m/s in still water. In which direction should the boat point its bow to travel directly across a 0.48-km wide river if the river flows at 2.5 m/s? What is the time interval for the trip? (b) A particle starts from rest and travels in a circular path of diameter 8.0 m. If the tangential component of its acceleration is 2.0 m/s2, what is the magnitude of its total acceleration the instant it has traveled halfway around the circle?
Please show all work and steps! Thanks!
Explanation / Answer
part A :
v^2 = u^2 - U^2
v^2 = 6.5^2 - 2.5^2
v = 6.5^2 - 2.5^2
v = 6 m/s
sin theta = 2.5/6.5
sin theta = 0.384
theta = 22.61 deg
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part B :
radial accleration a = v^2/R
a rad = 6.5^2/4 = 10.56 m/s^2
a tan = 2 m/s^2 ( given)
a total^2 = arad^2 + r tan^2
a total^2 = 10.56^2 + 2^2
a total = 10.75 rad/s^2
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