Beth leaves a dock in a motorboat travelling at 14 m/s. She heads downstream at an angle of 40° to the current, which flows at 6 m/s. Determine how long it takes for Beth to travel 400 m
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To determine how long it takes for Beth to travel 400 meters, we need to break down her speed into its horizontal and vertical components and then calculate the time it takes for her to cover the horizontal distance.
First, let's find the horizontal component of Beth's speed. This horizontal component is given by multiplying her speed by the cosine of the angle between her direction of motion and the x-axis.
Horizontal component of speed = Speed * cos(angle)
Horizontal component of speed = 14 m/s * cos(40°)
Next, let's find the vertical component of Beth's speed. This vertical component is given by multiplying her speed by the sine of the angle between her direction of motion and the x-axis.
Vertical component of speed = Speed * sin(angle)
Vertical component of speed = 14 m/s * sin(40°)
Now, let's determine the time it takes for Beth to cover the horizontal distance of 400 meters. We can calculate this time by dividing the horizontal distance by the horizontal component of Beth's speed.
Time = Distance / Horizontal component of speed
Time = 400 m / (14 m/s * cos(40°))
Calculating this expression will give us the time it takes for Beth to travel 400 m.