Bob heads out into a lake at an angle of 30�
with respect to the shore.
If his boat is capable of a speed of 3.3 m/s,
how far from land will he be in 9 min and
46 s ?
Answer in units of m
To find how far Bob will be from the land, we can use trigonometry and the speed of his boat. Here's what you can do to find the answer:
1. Convert the minutes and seconds into seconds. We have 9 minutes and 46 seconds, which is equal to 9 * 60 + 46 = 586 seconds.
2. We can use the formula: Distance = Speed * Time. Plug in the given speed of Bob's boat, which is 3.3 m/s, and the time in seconds, which is 586 seconds.
Distance = 3.3 m/s * 586 s
3. However, the boat is not moving directly towards the shore, but at an angle of 30 degrees. To find how far Bob will be from the land, we need to consider the distance in the direction perpendicular to the shore.
4. Use trigonometry to find the perpendicular distance. The perpendicular distance from the land is given by the formula: Perpendicular Distance = Distance * sin(angle), where the angle is given as 30 degrees.
Perpendicular Distance = (3.3 m/s * 586 s) * sin(30 degrees)
5. Now, use a calculator to calculate the sine of 30 degrees, which is 0.5.
Perpendicular Distance = (3.3 m/s * 586 s) * 0.5
6. Multiply the speed and time to get the distance in meters.
Perpendicular Distance = 3.3 m/s * 586 s * 0.5
7. Finally, calculate the result:
Perpendicular Distance = 966.9 meters
So, Bob will be approximately 966.9 meters away from the land.