In the vertical right triangle shown in Fig. 3.14, a particle falls from A to B either along the hypotenuse, or along the two legs (lengths a and b) via point C. There is no friction anywhere. A C b a (side view) Figure 3. B a) Estimate the time (call it t) if the particle travels along the hypotenuse? b) Evaluate the time (call it t₁) if the particle travels along the legs? Assume that at point C there is an infinitesimal curved arc that allows the direction of the particle's motion to change from vertical to horizontal without any change in speed. c) Justify that th=t₁ when a = 0. d) Assess how do the value of th and t₁ compare in the limit b << a?

In the vertical right triangle shown in Fig. 3.14, a particle falls from A to B either along the hypotenuse, or along the two legs (lengths a and b) via point C. There is no friction anywhere. A C b a (side view) Figure 3. B a) Estimate the time (call it t) if the particle travels along the hypotenuse? b) Evaluate the time (call it t₁) if the particle travels along the legs? Assume that at point C there is an infinitesimal curved arc that allows the direction of the particle's motion to change from vertical to horizontal without any change in speed. c) Justify that th=t₁ when a = 0. d) Assess how do the value of th and t₁ compare in the limit b << a?

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Description: In the vertical right triangle shown in Fig. 3.14, a particle falls from A to B either along thehypotenuse, or along the two legs (lengths a and b) via point C. There is no frictionanywhere.Aba(side view)Figure 3.Ba) Estimate the time (call it t) if

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Publisher:Raymond A. Serway, Chris Vuille

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Question

In the vertical right triangle shown in Fig. 3.14, a particle falls from A to B either along the
hypotenuse, or along the two legs (lengths a and b) via point C. There is no friction
anywhere.
A
b
a
(side view)
Figure 3.
B
a) Estimate the time (call it t) if the particle travels along the hypotenuse?
b) Evaluate the time (call it t₁) if the particle travels along the legs? Assume that at point
C there is an infinitesimal curved arc that allows the direction of the particle's motion
to change from vertical to horizontal without any change in speed.
c) Justify that t = t₁ when a = 0.
d) Assess how do the value of th and t₁ compare in the limit b << a?
e) Excluding the a = 0 case, conclude what triangle shape yields th
= t₁ ?

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