Application Giovanni is flying his Cessna airplane on a heading as shown. His instrument panel shows an air speed of 130 mi/h. (Air speed is the speed in still air without wind.) However, there is a 20 mi/h crosswind. What is the resulting speed of the plane?
To find the resulting speed of the plane, we can use the concept of vector addition.
The airspeed of the plane is the speed of the plane in still air, which is given as 130 mi/h.
The crosswind is a perpendicular component that acts at a right angle to the direction of the plane's heading. It has a magnitude of 20 mi/h.
To find the resulting speed, we can use the Pythagorean theorem:
Resulting Speed = √(airspeed^2 + crosswind^2)
Plugging in the given values, we get:
Resulting Speed = √(130^2 + 20^2)
Calculating this, we get:
Resulting Speed ≈ √(16900 + 400) ≈ √17300 ≈ 131.58 mi/h
So, the resulting speed of the plane is approximately 131.58 mi/h.
To find the resulting speed of the plane, we need to consider the effect of the crosswind on the plane's motion.
In this case, Giovanni's Cessna airplane has an air speed of 130 mi/h, which represents the speed of the plane in still air (without wind). Additionally, there is a 20 mi/h crosswind acting on the plane.
To determine the resulting speed, we can use the concept of vector addition. We can think of the airplane's motion as the combination of its air speed and the crosswind velocity.
To calculate the resulting speed, we need to find the magnitude of the resultant vector. The magnitude of a resultant vector can be found using the Pythagorean theorem.
Let's start by drawing a diagram to better understand the situation:
|\
| \ <- Air speed (130 mi/h)
W| \
| \
-----
In the diagram, the vertical line represents the air speed of the Cessna airplane (130 mi/h), and the slanted line represents the crosswind (20 mi/h).
Now, we can use the Pythagorean theorem to find the magnitude of the resulting speed:
Resulting speed^2 = air speed^2 + crosswind^2
Plugging in the values, we get:
Resulting speed^2 = (130 mi/h)^2 + (20 mi/h)^2
Calculating this equation would give us the square of the resulting speed.
To find the resulting speed, we take the square root of the calculated value:
Resulting speed = √((130 mi/h)^2 + (20 mi/h)^2)
Evaluating this equation would give us the final answer, which is the resulting speed of the Cessna airplane.
x component = 130
y component = 20
speed = sqrt (130^2 + 20^2)
direction
tan angle up from x = 20/130