A plane flying a its maximum speed can go 200 miles per hour with a tailwind and 160 miles per hour into a head wind.
a) What is the wind speed?
b) What would the maximum speed of the plane be if there was no wind?
the average of 200 and 160 is 180
so the speed of the plane with no wind is 180 mph,
and the wind speed is 20 mph
check:
going against the wind = 180-20 = 160
going with the wind = 180 + 20 = 200
To find the wind speed and the maximum speed of the plane with no wind, we can use the concept of relative velocity.
a) To find the wind speed, we can use the formula:
Wind Speed = (Plane's Maximum Speed with Tailwind - Plane's Maximum Speed into Headwind) / 2
Substituting the given values, we get:
Wind Speed = (200 mph - 160 mph) / 2
Wind Speed = 40 mph / 2
Wind Speed = 20 mph
Therefore, the wind speed is 20 mph.
b) To find the maximum speed of the plane with no wind, we need to consider the concept of ground speed.
Ground Speed = Plane's Maximum Speed with Tailwind - Wind Speed
Substituting the known values, we get:
Ground Speed = 200 mph - 20 mph
Ground Speed = 180 mph
Therefore, the maximum speed of the plane with no wind is 180 mph.
To solve this problem, we need to understand the relationship between the plane's speed and the wind speed.
a) To calculate the wind speed, we can use the concept of the relative velocity of the plane with respect to the ground. When the plane flies with a tailwind, the apparent speed of the plane is the sum of the plane's speed and the wind speed. On the other hand, when the plane flies against a headwind, the apparent speed of the plane is the difference between the plane's speed and the wind speed.
Therefore, we can set up two equations using the given speeds:
1. When flying with a tailwind: Plane's speed + Wind speed = 200 mph
2. When flying against a headwind: Plane's speed - Wind speed = 160 mph
We can solve this system of equations to find the wind speed.
b) To determine the maximum speed of the plane with no wind, we need to find the average of the maximum speed with a tailwind and the maximum speed against a headwind. Since the average of two numbers is the sum of the numbers divided by 2, we can calculate it by using the formula:
Maximum speed with no wind = (Maximum speed with a tailwind + Maximum speed against a headwind) / 2
Let's solve these equations step-by-step to find the answers:
a)
Equation 1: Plane's speed + Wind speed = 200 mph
Equation 2: Plane's speed - Wind speed = 160 mph
By adding both equations, we can eliminate the wind speed:
(Plane's speed + Wind speed) + (Plane's speed - Wind speed) = 200 mph + 160 mph
2 * Plane's speed = 360 mph
Plane's speed = 360 mph / 2
Plane's speed = 180 mph
Now we can substitute this value back into either of the initial equations to find the wind speed. Let's use Equation 1:
180 mph + Wind speed = 200 mph
Wind speed = 200 mph - 180 mph
Wind speed = 20 mph
Therefore, the wind speed is 20 mph.
b)
Maximum speed with no wind = (Maximum speed with a tailwind + Maximum speed against a headwind) / 2
Maximum speed with no wind = (200 mph + 160 mph) / 2
Maximum speed with no wind = 360 mph / 2
Maximum speed with no wind = 180 mph
Therefore, the maximum speed of the plane with no wind is 180 mph.