3. (From an old exam) Bernice and her friend Amelia are on a long hiking trip when they come to a river. The width of the river is d = 1.0 mile. They are currently at point A in the picture below; directly across the river, at point B, is a perfect-looking campsite.
3. (From an old exam) Bernice and her friend Amelia are on a long hiking trip when they come to a river. The width of the river is d = 1.0 mile. They are currently at point A in the picture below; directly across the river, at point B, is a perfect-looking campsite.
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3 D only please, show work
Transcribed Image Text:3. (From an old exam) Bernice and her friend Amelia are on a long hiking trip when they come to a river. The
width of the river is d = 1.0 mile. They are currently at point A in the picture below; directly across the river, at
point B, is a perfect-looking campsite.
B
d
W
N
S
E
A
Bernice and Amelia know that they can paddle their inflatable raft at a rate of 2.5 mi/hr (with respect to
the water) and walk at 4.0 mi/hr (with respect to the ground). With some investigation, they discover that the
current in the river is flowing at 2.0 mi/hr toward the west. They discuss what would be the fastest way to cross
the river.
Amelia says, "If we get in the raft and head straight north with respect to the water, the current will carry
us to the west, so that our velocity with respect to the ground will be at some angle west of north. Thus, we
will end up somewhere west of point B. We can then walk back eastward along the bank until we reach point B.
We can walk faster than we can paddle the raft, so this should be the quickest way to get to B."
CONTINUED ON NEXT PAGE
a) On the grid below, draw a vector diagram showing the velocity of Amelia (in the raft) with respect to
the water (A/W), the water's velocity with respect to the ground (w/G), and Amelia's resultant velocity with
respect to the ground (A/G). Let each square in the grid represent 0.5 mi/hr.
b) How long will it take Amelia to cross the river? (Hint: how far does she travel with respect to the water?)
c) How far west of point B would Amelia end up after crossing the river? How long would it take her to walk
this distance?
Transcribed Image Text:Bernice says, "I think it might be faster if we took the raft directly to point B. We could head somewhat east
of north with respect to the water, so that our velocity with respect to the ground would be straight north."
d) On the grid below, draw a vector diagram showing the velocity of Bernice (in the raft) with respect to
the water (B/w), the water's velocity with respect to the ground (w/G), and Bernice's resultant velocity with
respect to the ground (B/G). Let each square in the grid represent 0.5 mi/hr.
e) What would be Bernice's speed with respect to the ground? How long would it take her to get to point B?
Whose method is faster?
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