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Crossing a River (Vectors Question)?
A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river. The river is 800 m wide.
In which direction should the motorboat head in order to reach a point on the opposite bank directly east from the starting point? (The boat's speed relative to the water is 4.2 m/s)
What is the velocity of the boat relative to the earth?
How much time is required to cross the river?
1 Answer
- Anonymous1 decade agoFavorite Answer
Let:
u be the boat's velocity relative to the water,
a be its angle east of north,
v be the downstream velocity of the river,
t be the time to cross the river.
w be the width of the river.
Parallel to the river:
u cos(a) = v
cos(a) = v / u
= 2.0 / 4.2
a = 61.563 deg.
The boat should head N 61.6 deg E to 3 sig. fig.
The boat's velocity relative to earth is:
u sin(a) = 4.2 sin(a)
= 3.69 m/s to 3 sig. fig. directly east.
Across the river:
ut sin(a) = w
t = w / [ u sin(a) ]
t = 800 / [ 4.2 sin(a) ]
= 217 sec to 3 sig. fig.