Concept explainers
Airplanes A and B are flying at the same altitude and are tracking the eye of hurricane C. The relative velocity of C with respect to A is vC/A = 350 km/h ⦫ 75°, and the relative velocity of C with respect to B is vC/B = 400 km/h ⦪ 40°. Determine (a) the relative velocity of B with respect to A, (b) the velocity of A if ground-based
Fig. P11.121
(a)
The relative velocity
Answer to Problem 11.121P
The relative velocity
Explanation of Solution
Given Information:
The relative velocity
The relative velocity
Calculation:
Show the relative velocity vector diagram of airplanes with respect to hurricane as in Figure (1).
Write the relative velocity of hurricane with respect to airplane A:
Here,
Write the relative velocity of hurricane with respect to airplane B:
Here,
Equate equations (1) and (2).
Write the relative velocity of airplane B with respect to airplane A:
Here,
Substitute equation (4) in equation (3).
Calculate relative velocity B with respective to A by applying law of cosine for Figure (1).
Here,
Substitute
Calculate the angle
Here,
Substitute
Write the angle subtended by
Here, angle subtended by
Substitute
Therefore, the relative velocity
(b)
The velocity
Answer to Problem 11.121P
The velocity
Explanation of Solution
Given Information:
The relative velocity
The relative velocity
Calculation:
Rewrite Equation (1):
Write vector
Choose direction of
Substitute
Calculate the resultant velocity
Here,
Substitute
Calculate the angle
Substitute
Therefore, the velocity
(c)
The change in position
Answer to Problem 11.121P
The change in position
Explanation of Solution
Given Information:
The relative velocity
The relative velocity
Calculation:
Write the position of airplane B as:
Here,
Write the position of hurricane as:
Here,
Write the position of hurricane with respect to airplane B as:
Here,
Use Equations (8) and (9) to rewrite Equation (10)
Write the change in position of hurricane with respect to B as:
Here,
Rewrite Equation (11) using Equation (12) as:
Calculate the change in position
Substitute
Therefore, the change in position
Want to see more full solutions like this?
Chapter 11 Solutions
Connect 2 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
- two automobiles A and B are approaching each other in adjacent highway lanes. at t=0, A and B are 3200ft apart. Their speeds are Va= 65 mi/h and Vb= 40 mi/h, and they are at points P and Q, respectively. knowing that A passes point Q 40s after B was there and that B passes point P 42s after A was there: A) determine the speed of B at the moment that it passes A in ft/s B.) when the vehicles pass each other in seconds C.) uniform acceleration of B in ft/s^2arrow_forwardThe airplane above now moves due east while the alien pilot points the plane somewhat south of east, toward a steady wind that blows to the northeast. The plane Phas velocity ⃗vP W relative to the wind W , with an airspeed (speed relative to the wind) of 215 km/h, directed at angle θ south of east. The wind has velocity ⃗vWG relative to the ground G with speed 65.0 km/h, directed 20.0◦ east of north. What is the magnitude of the velocity ⃗vP G of the plane relative to the ground, and what is θ?arrow_forwardCar A is moving with constant speed v on the straight and level highway. The police officer in the stationary car P attempts to measure the speed v with radar. If the radar measures “line-of sight” velocity, what velocity v' will the officer observe? Evaluate your general expression for the values v = 74 mi/hr, L = 605 ft, and D = 19 ft, and draw any appropriate conclusions.arrow_forward
- During a flyby of the earth, the velocity of a spacecraft is 10.4 km/s as it reaches its minimum altitude of 990 km above the surface at point A. At point B the spacecraft is observed to have an altitude of 8350 km. Determine (a) the magnitude of the velocity at point B, (b) the angle φB.arrow_forwardA model airplane flies over an observer O with constant speed in a straight line as shown. Determine the signs (positive [p], negative [n], or zero [z]) for r,r˙,r¨,θ,θ˙, and θ¨ for each of the positions A, B, and C.arrow_forwardIn a game of pool, ball A is moving with a velocity v0 when it strikes balls B and C, whichare at rest and aligned as shown. Knowing that after the collision the three balls move inthe directions indicated and that v0 = 12 ft/s and vC= 6.29 ft/s, determine the magnitude ofthe velocity of (a) ball A, (b) ball B.arrow_forward
- A golf ball is struck with a velocity of 80 ft/s as shown. Determine the speed at which it strikes the ground at B and the time of flight from A to B.arrow_forward-Car A moving at a constant velocity of 25 m/sec passes a gasoline station. At the same instant, car B leaves the same gasoline station and travels the same direction as that of car A. Determine the required acceleration of car B in order to overtake car A after 35 seconds. -Two cars A and B are travelling in the same direction with a velocity of 30 m/sec. Car A is 250 meters behind car B. After 17 seconds, car B decelerates at a constant rate. Determine the deceleration of car B so that car A can overtake after 17 seconds.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY