Bob heads out into a lake at an angle of 27◦
with respect to the shore.
If his boat is capable of a speed of 1.3 m/s,
how far from land will he be in 2 min and
28 s ?
Answer in units of m.
1.3m/s * 148s * sin 27° = 87.3m
To solve this problem, we can break it down into smaller steps:
Step 1: Convert the angle from degrees to radians.
To do this, multiply the angle by π/180.
In this case, 27◦ * π/180 = 0.471 radians.
Step 2: Calculate the distance Bob travels in 2 minutes and 28 seconds.
Convert 2 minutes and 28 seconds to seconds:
2 minutes * 60 seconds/minute = 120 seconds
120 seconds + 28 seconds = 148 seconds
To find the distance, we can use the formula:
Distance = Speed * Time
Distance = 1.3 m/s * 148 s = 192.4 meters
Step 3: Find the distance Bob will be from the land.
To find this distance, we need to consider the distance Bob traveled perpendicular to the shore.
Using trigonometry, we can find this distance using the formula:
Distance from land = Distance * sin(angle)
Distance from land = 192.4 m * sin(0.471) ≈ 92.879 meters
Therefore, Bob will be approximately 92.879 meters from the land.