Kym is in a boat traveling 3.8 m/s straight across a river 240 m wide. The river is flowing at 1.6 m/s.
a) What is Kym’s resultant velocity?
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b) How long does it take Kym to cross the river?
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c) How far is Kym downstream when she reaches the other side?
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i think you go to my school we have the same exact questions lol
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To find the answers to these questions, we need to use vector addition and some basic formulas from physics. Let's break it down step by step:
a) To find Kym's resultant velocity, we need to add the velocities of the boat and the river. Since the boat is traveling straight across the river, the vertical component of the boat's velocity is zero. Therefore, we only need to consider the horizontal component:
Boat's horizontal velocity = 3.8 m/s
River's velocity = 1.6 m/s
To find the resultant velocity, we use the Pythagorean theorem:
Resultant velocity = √(boat's velocity^2 + river's velocity^2)
Resultant velocity = √(3.8^2 + 1.6^2)
Resultant velocity ≈ √(14.44 + 2.56)
Resultant velocity ≈ √17
Resultant velocity ≈ 4.12 m/s
Therefore, Kym's resultant velocity is approximately 4.12 m/s.
b) To find the time it takes for Kym to cross the river, we can use the formula:
Time = Distance / Velocity
Since the distance is given as 240 m and the resultant velocity is 4.12 m/s:
Time = 240 m / 4.12 m/s
Time ≈ 58.25 seconds
Therefore, it takes Kym approximately 58.25 seconds to cross the river.
c) To find how far downstream Kym is when she reaches the other side, we can use the formula:
Distance downstream = River's velocity * Time
Since the river's velocity is 1.6 m/s and the time is 58.25 seconds:
Distance downstream = 1.6 m/s * 58.25 s
Distance downstream ≈ 93.2 meters
Therefore, Kym is approximately 93.2 meters downstream when she reaches the other side.