Wind can affect the speed of an airplane. Suppose a plane is flying
round-trip from New York City to San Francisco.The plane has a
cruising speed of 300 miles per hour.The wind is blowing from west to
east at 30 miles per hour.
When the plane flies into (in the opposite direction of) the wind, its
speed decreases by 30 miles per hour.When the plane flies with (in the
same direction as) the wind, its speed increases by 30 miles per hour.
a. The distance between New York City and San Francisco is
3,000 miles. Make a table that shows the total time the plane has
traveled after each 200-mile interval on its trip from New York City
to San Francisco and back.
well, you know that flying east-to-west, the plane goes 270 mi/hr
going to the east, it flies at 330 mi/hr.
So, just make your table for each 200-mile interval. That's 15 entries in each direction.
To calculate the total time the plane has traveled after each 200-mile interval on its trip from New York City to San Francisco and back, we need to consider the effect of wind on the plane's speed.
Given:
- Cruising speed of the plane: 300 miles per hour
- Wind speed: 30 miles per hour
- Distance between New York City and San Francisco: 3,000 miles
To create the table, we'll calculate the effective speed of the plane at each interval, taking into account the wind's direction.
Let's start by calculating how the wind affects the plane's speed in the different directions:
1. Flying into the wind (opposite direction):
Effective speed = Cruising speed - Wind speed
= 300 - 30
= 270 miles per hour
2. Flying with the wind (same direction):
Effective speed = Cruising speed + Wind speed
= 300 + 30
= 330 miles per hour
Now, let's create the table:
| Distance Interval (miles) | Effective Speed (mph) | Time Taken (hours) |
|--------------------------|-----------------------|--------------------|
| 0 - 200 | 270 | 0.74 |
| 200 - 400 | 330 | 0.61 |
| 400 - 600 | 270 | 0.74 |
| 600 - 800 | 330 | 0.61 |
| 800 - 1000 | 270 | 0.74 |
| 1000 - 1200 | 330 | 0.61 |
| 1200 - 1400 | 270 | 0.74 |
| 1400 - 1600 | 330 | 0.61 |
| 1600 - 1800 | 270 | 0.74 |
| 1800 - 2000 | 330 | 0.61 |
| 2000 - 2200 | 270 | 0.74 |
| 2200 - 2400 | 330 | 0.61 |
| 2400 - 2600 | 270 | 0.74 |
| 2600 - 2800 | 330 | 0.61 |
| 2800 - 3000 | 270 | 0.74 |
|--------------------------|-----------------------|--------------------|
To create a table showing the total time the plane has traveled after each 200-mile interval on its trip from New York City to San Francisco and back, we need to consider the effect of wind on the plane's speed.
First, let's calculate the plane's effective speed in different scenarios:
1. Flying into the wind:
The plane's cruising speed is 300 mph, but since the wind is blowing from west to east at 30 mph, the effective speed of the plane will be 300 - 30 = 270 mph.
2. Flying with the wind:
The plane's cruising speed is still 300 mph, but since the wind is blowing from west to east at 30 mph, the effective speed of the plane will be 300 + 30 = 330 mph.
Now, let's create the table:
| Distance (miles) | Effective Speed (mph) | Time (hours) |
|-------------------|-----------------------|--------------|
| 200 | 270 | 0.74 |
| 400 | 270 | 1.48 |
| 600 | 270 | 2.22 |
| 800 | 270 | 2.96 |
| 1000 | 270 | 3.70 |
| 1200 | 270 | 4.44 |
| 1400 | 270 | 5.19 |
| 1600 | 270 | 5.93 |
| 1800 | 270 | 6.67 |
| 2000 | 270 | 7.41 |
| 2200 | 330 | 6.67 |
| 2400 | 330 | 7.27 |
| 2600 | 330 | 7.88 |
| 2800 | 330 | 8.48 |
| 3000 | 330 | 9.09 |
In the table, the distance column represents the cumulative distance traveled (e.g., at 200 miles, 400 miles, 600 miles, etc.). The effective speed column represents the speed of the plane after accounting for the wind's effect. Finally, the time column represents the total time the plane has traveled after each 200-mile interval.
Note that the time calculation is done by dividing the distance by the effective speed. For example, for the first row, the time is calculated as 200 miles / 270 mph = 0.74 hours.
This table covers the plane's round trip from New York City to San Francisco, considering the impact of wind on its speed.