For Exercises 65-68, find the work w done by a force F in moving an object in a straight line given by the displacement vector D. (See Example 6) F = 40 i − 15 j lb ; D = 30 i + 10 j ft
For Exercises 65-68, find the work w done by a force F in moving an object in a straight line given by the displacement vector D. (See Example 6) F = 40 i − 15 j lb ; D = 30 i + 10 j ft
For Exercises 65-68, find the work w done by a force F in moving an object in a straight line given by the displacement vector D. (See Example 6)
F
=
40
i
−
15
j
lb
;
D
=
30
i
+
10
j
ft
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
[A] A force F has a magnitude of 15 newtons and has the same direction (but different magnitude)
as the vector v = 2i+j+ 2k. This force pushes an object on a ramp in a straight line from the
point P(4, 2, 5) to the point Q (5, 4, 8), where the coordinates are measured in meters.
(A.1) Find the force F by writing it in terms of the standard unit vectors, i, j, and k.
(A.2) Determine how much work is done by the force in moving the object from P to Q as
described above. Round your answer to the nearest tenth of the approprite units.
A ski jumper travels down a slope of the height H and leaves the ski track moving in the horizontal direction. The only force acting on the ski jumper is gravity. Find the height of the ski track h at which the ski jumper flies the longest distance.
The figure shows a potted plant acted on by four forces. Evaluate the vector
product between forces 2 and 3 if 0 = 68°, 140, F₁ = 12 N, F₂ = 18 N.
F3 = 11 N, and F4 = 19 N.
For the direction, indicate a vector product out of the screen as positive and a
vector product into the screen as negative.
F₁.
F₂
University Calculus: Early Transcendentals (3rd Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY