Mary needs to row her boat across a 120 m -wide river that is flowing to the east at a speed of 1.4 m/s. Mary can row the boat with a speed of 2.0 m relative to the water.
1. How long does it take Mary to reach the opposite river bank ?
2.If Mary rows straight north, how far downstream will she land?
To find the answers, we can use the concept of relative velocity.
1. How long does it take Mary to reach the opposite river bank?
We can break down Mary's motion into two components: her velocity relative to the water and the velocity of the river. Since Mary rows straight across the river, her velocity relative to the ground will be perpendicular to the river's velocity.
Let's denote:
- Mary's velocity relative to the water as v_boat = 2.0 m/s (eastward)
- The river's velocity as v_river = 1.4 m/s (eastward)
- The width of the river as d = 120 m
To find the time taken, we divide the distance she needs to cross by her velocity relative to the ground:
Time = Distance / Velocity
The distance Mary needs to cross is the same as the width of the river:
Distance = 120 m
To calculate Mary's velocity relative to the ground, we need to find the vector sum of her velocity relative to the water and the river's velocity. Since they are perpendicular, we can use the Pythagorean theorem:
Velocity^2 = (v_boat)^2 + (v_river)^2
Velocity = sqrt((2.0 m/s)^2 + (1.4 m/s)^2)
Time = Distance / Velocity
Time = 120 m / Velocity
Now we can calculate the time it takes for Mary to reach the opposite river bank by substituting the values into the formula:
Time = 120 m / (sqrt((2.0 m/s)^2 + (1.4 m/s)^2))
2. If Mary rows straight north, how far downstream will she land?
If Mary rows straight north, her velocity relative to the ground will only be in the y-direction, perpendicular to the river's velocity.
Since Mary is not influenced by the river's velocity in this case, the distance downstream will be zero.
Therefore, if Mary rows straight north, she will not be carried downstream by the river. She will land exactly opposite to her starting point.
I hope this helps! Let me know if you have any further questions.
To answer these questions, we need to consider the velocities and distances involved.
1. To calculate the time it takes for Mary to reach the opposite river bank, we can divide the width of the river by the velocity of Mary's boat relative to the water. This is because the velocity of the river does not affect the time taken to cross the river.
The velocity of the river does, however, affect the direction in which Mary will end up relative to the opposite bank. In this case, the river is flowing east at a speed of 1.4 m/s. So, when Mary rows straight across, her boat will also be carried downstream by the river's flow.
Let's calculate the time it takes for Mary to reach the opposite river bank.
Time = Distance / Velocity
Time = 120 m / (2.0 m/s)
Time = 60 seconds
Therefore, it will take Mary 60 seconds to reach the opposite river bank.
2. To calculate how far downstream Mary will land if she rows straight north, we need to consider how the river's flow affects her position.
Since the river is flowing east, after Mary reaches the opposite bank, she will be downstream of her intended landing spot. We can calculate this distance using the formula:
Distance = Time x Velocity
In this case, the time is still 60 seconds, but the velocity now includes the river's flow since Mary's boat will be carried downstream as she rows north.
Distance = 60 seconds x (2.0 m/s + 1.4 m/s)
Distance = 60 seconds x 3.4 m/s
Distance = 204 meters
Therefore, if Mary rows straight north, she will land approximately 204 meters downstream from her intended landing spot due to the river's flow.
Look at this in directions.
She rows North at 2.0m/s, and the distance is 120M North.
time= distanceN/speedN= 120m/2.0m/s=60sec
Where does she land. YOu have 2.0m/s across, downstream 1.4m/s
In 60 seconds, she goes distance=1.4*60 m