For this assignment, refer to: http://www.physicsclassroom.com/class/vectors/Les
ID: 1789692 • Letter: F
Question
For this assignment, refer to: http://www.physicsclassroom.com/class/vectors/Lesson-1/Relative-Velocity-and-Riverboat-Problems, as discussed during the lecture for Chapter 4.
Re-do the plane problem such that the plane is now traveling 150km/hr and increase the tail, head, and side wind velocities to 75km/hr, 100km/hr and 50km/hr, respectively. Re-compute the plane velocity for the three cases (tailwind, headwind, and side wind).
Re-do the motorboat problem such that the river is moving with a velocity of 20 m/s, North and the motorboat is moving with a velocity of 15 m/s, East.
What is the resultant velocity of the motorboat?
If the width of the river is 200 meters wide, then how much time does it take the boat to travel shore to shore?
What distance downstream does the boat reach the opposite shore?
Carefully proof your work for grammar and spelling. Submit your work in MS Word file format and include your Name, Course Info Assignment Number and Date in your submission. Late submissions will not be accepted. Your work will be checked for plagiarism and copying. WARNING: Plagiarism and copying will result in a zero for the assignment. Multiple incidents of plagiarism and copying in the course will result in a grade of E for the course and a submission of a VAIR to university officials.
Explanation / Answer
Plane problem
let the plane be flying in x direction, and i, j and k be unit vectors in x, y and z directions
then
tailwind Vt = 75i km/hr
headwind Vh= -100i km/hr
sidewind Vs= 50j km/hr
Plane speed, V = 150i km/hr
so Plane velocity for the tailwind case = V' = V + Vt = 150 + 75 = 225 km/hr
Plane velocity for headwind case, V' = V + Vh = 150 - 100 = 50 km/hr
Plane velocity for sidewind , V' = V + Vs = 150i + 50j
|V'| = sqroot(150^2 + 50^2) = 158.113 km/hr
angle made with the direction of motion of the plane relative to the wind = theta
tan(theta) = Vs/V = 50/150 = 1/3
theta = 18.43 deg
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