A boat on a lake is launched with an initial speed vo. The boat experiences a drag force from the water 6) F₁ = -beavû, where b and a are positive constants and û is unit vector in the direction of velocity. There are no other frictional forces acting on the boat. (a) Draw a free body diagram and use Newton's second law to determine the differential equations describing the boat's motion. (b) Solve the differential equations for the speed of the boat v(t). (c) Show that the time for the boat to come to rest is t = (m/ab)(1 — e¯avo).
A boat on a lake is launched with an initial speed vo. The boat experiences a drag force from the water 6) F₁ = -beavû, where b and a are positive constants and û is unit vector in the direction of velocity. There are no other frictional forces acting on the boat. (a) Draw a free body diagram and use Newton's second law to determine the differential equations describing the boat's motion. (b) Solve the differential equations for the speed of the boat v(t). (c) Show that the time for the boat to come to rest is t = (m/ab)(1 — e¯avo).
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A boat on a lake is launched with an initial speed vo. The boat experiences a drag force
from the water
Fd=-beavû,
where b and a are positive constants and û is unit vector in the direction of velocity. There are no
other frictional forces acting on the boat.
(a) Draw a free body diagram and use Newton's second law to determine the differential equations
describing the boat's motion.
(b) Solve the differential equations for the speed of the boat v(t).
(c) Show that the time for the boat to come to rest is t = (m/ab)(1-e-avo).
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