Calculating Resultant Velocity of Plane: Kinematic Questions

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In summary, the problem involves a pilot flying due east at a speed of 75 m/s while a wind blows at 60 degrees North East with a constant speed of 25 m/s. To find the resultant velocity of the plane, the velocities must be expressed as rectangular vectors and added using the cosine rule. The resultant velocity can then be calculated using the formula: resultant velocity^2 = 75^2 + 25^2 - 2(75)(25) cos 150, in degrees.
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Homework Statement


A pilot heads his airplane due east at a speed of 75 m/s. While he is flying, a wind blows at 60 degrees North East with a constant speed of 25 m/s. What is the reultant velocity of the plane?


Homework Equations


s=(u+v/2)t, v=u+at, and s=ut+1/2at²


The Attempt at a Solution


(none as of yet... I am completely stumped... my professor just threw this onto us without giving us any previous info and I've searched everywhere for the answer, textbook, internet and i went to him and he was just like do it yourself)
 
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  • #2
Express both velocities as rectangular vectors and use vector addition.
 
  • #3
Draw a vector triangle and use the cosine rule.

resultant velocity^2 = 75^2 + 25^2 - 2(75)(25) cos 150, in degrees.
 
  • #4
thank you so much mate... this site is a life saver... like a professor here helping me 24/7 much appreciated
 

Related to Calculating Resultant Velocity of Plane: Kinematic Questions

1. How do you calculate the resultant velocity of a plane?

To calculate the resultant velocity of a plane, you need to use the vector addition method. This involves breaking down the velocities into their horizontal and vertical components, adding them separately, and then using the Pythagorean theorem to find the resultant velocity.

2. What is the difference between velocity and speed?

Velocity is a vector quantity that includes both the speed and direction of motion, while speed is a scalar quantity that only represents the magnitude of motion. In other words, velocity tells you how fast and in what direction an object is moving, while speed only tells you how fast it is moving.

3. How does the angle of the plane affect its resultant velocity?

The angle of the plane affects the horizontal and vertical components of its velocity. If the plane is flying at an angle, some of its velocity will be directed horizontally, while the rest will be directed vertically. The angle also affects the magnitude of the resultant velocity, as it can make it larger or smaller depending on the direction of the plane's motion.

4. Can the resultant velocity of a plane be negative?

Yes, the resultant velocity of a plane can be negative. This means that the plane is moving in the opposite direction of its initial velocity. For example, if a plane is flying east at a velocity of 100 km/h, a negative resultant velocity would mean that the plane is now flying west at a velocity of 100 km/h.

5. What other factors may affect the resultant velocity of a plane?

Other factors that may affect the resultant velocity of a plane include wind speed and direction, air resistance, and the weight and aerodynamics of the plane. These factors can either increase or decrease the resultant velocity, depending on their specific effects on the plane's motion.

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