Suppose that a boat weighs 1000 pounds and is on a ramp inclined at 30°, Represent the force due to gravity, F, using F= - 1000j as shown in the figure to the right. a. Write a unit vector along the ramp in the upward direction. b. Find the vector projection of F onto the unit vector from part a. c. What is the magnitude of the vector projection in part b? What does this represent? V3 a. The unit vector along the ramp in the upward direction is u = (Simplify your answer. Type your answer in terms of i and j. Use integers or fractions for any numbers in the expression. Rationalize all denominators. Type an exact answer, using radicals as needed.) b. proj,F= - 250/3i- 250 (Simplify your answer, Type your answer in terms of i and j. Rationalize all denominators. Type an exact answer, using radicals as needed.) c. The magnitude of vector projection proj, F is 500'. (Simplify your answer. Round to the nearest whole number as needed.) What does the magnitude of vector projection proj, F represent? Question is complete. Tap on the red indicators to see incorrect answers.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 31E
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X6.7.63
Suppose that a boat weighs 1000 pounds and is on a ramp
inclined at 30°. Represent the force due to gravity, F, using
F= - 1000j as shown in the figure to the right.
a. Write a unit vector along the ramp in the upward direction.
b. Find the vector projection of F onto the unit vector from part a.
c. What is the magnitude of the vector projection in part b? What
does this represent?
V3
a. The unit vector along the ramp in the upward direction is u =
i+
(Simplify your answer. Type your answer in terms of i and j. Use integers or fractions for any numbers in the expression. Rationalize all denominators. Type an exact answer, using radicals as needed.)
b. proj„F = - 2503i- 250j
(Simplify your answer. Type your answer in terms of i and j. Rationalize all denominators. Type an exact answer, using radi
as needed.)
c. The magnitude of vector projection proj, F is 500'.
(Simplify your answer. Round to the nearest whole number as needed.)
What does the magnitude of vector projection proj, F represent?
Question is complete. Tap on the red indicators to see incorrect answers.
Transcribed Image Text:X6.7.63 Suppose that a boat weighs 1000 pounds and is on a ramp inclined at 30°. Represent the force due to gravity, F, using F= - 1000j as shown in the figure to the right. a. Write a unit vector along the ramp in the upward direction. b. Find the vector projection of F onto the unit vector from part a. c. What is the magnitude of the vector projection in part b? What does this represent? V3 a. The unit vector along the ramp in the upward direction is u = i+ (Simplify your answer. Type your answer in terms of i and j. Use integers or fractions for any numbers in the expression. Rationalize all denominators. Type an exact answer, using radicals as needed.) b. proj„F = - 2503i- 250j (Simplify your answer. Type your answer in terms of i and j. Rationalize all denominators. Type an exact answer, using radi as needed.) c. The magnitude of vector projection proj, F is 500'. (Simplify your answer. Round to the nearest whole number as needed.) What does the magnitude of vector projection proj, F represent? Question is complete. Tap on the red indicators to see incorrect answers.
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