If a vector that is 1cm long represents a velocity of 10km/h, what velocity does a vector 2cm long drawn to the same scale represent?
An airplane has an airspeed of 100km/h north. If there is a 30 km/h tailwind, what is its groundspeed?
1. V = 2 * 10km/h = 20km/h.
2. V = 100km/h + 30km/h = 130km.
Well, if a vector that is 1cm long represents a velocity of 10km/h, then a vector that is 2cm long would represent a velocity of 20km/h. It's like doubling the size of your ice cream scoop - more velocity, more fun!
As for the airplane, it's got an airspeed of 100km/h north and a 30 km/h tailwind. So, let me do some math while juggling these numbers. Now, let's add the airspeed and the tailwind speed together - 100 + 30. *Calculates while juggling* That gives us 130 km/h. So, the groundspeed will be 130 km/h. That's one fast-flying airplane, zooming through the sky with style!
To solve the first question, we can use proportions to find the velocity represented by a vector 2cm long.
Let's set up the proportion:
1 cm -> 10 km/h
2 cm -> x km/h
Using cross-multiplication, we can solve for x:
1 * x = 2 * 10
x = 20 km/h
Therefore, a vector 2cm long represents a velocity of 20 km/h.
For the second question, we need to calculate the groundspeed of the airplane, given its airspeed and the speed of the tailwind.
The groundspeed is calculated by adding the airspeed and tailwind speed since they are in the same direction.
Groundspeed = Airspeed + Tailwind speed
Groundspeed = 100 km/h + 30 km/h
Groundspeed = 130 km/h
Therefore, the groundspeed of the airplane is 130 km/h.
To find the velocity represented by a vector of a different length, we can set up a proportion using the given information.
Let's assume that the scale is linear, which means if the length of the vector is multiplied by a certain factor, the velocity it represents will also be multiplied by the same factor.
In the first question, we are given that a vector of 1cm represents a velocity of 10km/h. So, we can set up the proportion as follows:
1cm / 10km/h = 2cm / x km/h
To solve for x, we cross multiply and solve for x:
1cm * x km/h = 10km/h * 2cm
x = (10km/h * 2cm) / 1cm
x = 20 km/h
Therefore, a vector 2cm long drawn to the same scale represents a velocity of 20km/h.
Moving on to the second question,
Groundspeed is the combination of airspeed and wind speed. When an airplane has a tailwind, it means the wind is blowing in the same direction as the airplane's flight. In this case, the tailwind adds to the airspeed to increase the groundspeed.
Given:
Airspeed = 100km/h north
Tailwind = 30km/h
To find the groundspeed, we simply add the airspeed and tailwind:
Groundspeed = Airspeed + Tailwind
Groundspeed = 100km/h + 30km/h
Groundspeed = 130km/h
Therefore, the groundspeed of the airplane is 130km/h.