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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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