Concept explainers
An aircraft flies at constant altitude (with respect to sea level) over the South Rim of the Grand Canyon (Fig. P3.40, page 83). Consider a coordinate system such that the positive x axis points to the east, and the positive y axis points north. The aircraft’s initial position and velocity are 1350 m at an angle of 145° and 60.0 m/s at an angle of 55.0° where both angles are measured counterclockwise with respect to the positive x axis. The aircraft’s acceleration is 4.0 m/s2 at an angle of 195° with respect to the positive x axis. a. What is the velocity of the aircraft after 7.50 s have elapsed? b. What is the position vector of the aircraft after 7.50 s have elapsed?
(a)
The velocity of the aircraft after
Answer to Problem 14PQ
The velocity of the aircraft after
Explanation of Solution
An aircraft flies at constant altitude with initial position of
The two-dimensional motion of an object can be described using the components of a vector with magnitude and direction given by
The position of the aircraft is
The velocity of the aircraft is
The acceleration of the aircraft is
Write the formula for the velocity vector [two-dimensional kinematic equation]
Here,
Conclusion:
Substitute
Thus, the velocity of the aircraft after
(b)
The position of the aircraft after
Answer to Problem 14PQ
The position of the aircraft after
Explanation of Solution
Write the formula for the position vector [two-dimensional kinematic equation]
Here,
Conclusion:
Substitute
Thus, The position of the aircraft after
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Chapter 4 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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