Crossing the River I. A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is 4.2 m/s due east. The river is 500 m wide. (a) What is your velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of your starting point will you reach the opposite bank?
Crossing the River I. A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is 4.2 m/s due east. The river is 500 m wide. (a) What is your velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of your starting point will you reach the opposite bank?
Crossing the River I. A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is 4.2 m/s due east. The river is 500 m wide. (a) What is your velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of your starting point will you reach the opposite bank?
Several people stand on a bridge over a river. The bridge is not level, so the people are all different heights above the river. Each person throws a stone to the river.
a) The first person is 26.8 m above the river and throws her stone with a speed of 16.6 m/s at an angle of 6 degrees to the horizontal (positive degrees are above horizontal, negative degrees are below). How long does it take her stone to hit the water, in seconds?
b) The second person is 19.0 m above the river and throws his stone with a speed of 17.1 m/s at an angle of -21.4 degrees to the horizontal (positive degrees are above horizontal, negative degrees are below). What is the range of his stone, in meters?
c)The third person is 9.1 m above the river and throws their stone with a speed of 6.5 m/s at an angle of 9.3 degrees to the horizontal (positive degrees are above horizontal, negative degrees are below). What is the speed of this stone (in m/s) just before it strikes the river?
A 425 m wide river flows North at 2.0 m/s. A turtle points himself directly East and swims at 8.0 m/s.
How long will it take to cross the river?
How far downriver does he end up?
What is his resultant velocity as he crosses the river?
What heading should he take in order to head directly East?
How long will take to cross the river in this case?
The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of 2.3 m/s in a direction 28° east of north relative to the Earth. It encounters a wind that has a velocity of 4.5 m/s in a direction of 45° south of west relative to the Earth.
What is the magnitude of the velocity of the wind relative to the water, in meters per second?
What is the angle of the velocity of the wind relative to the water degrees south of west?
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