A calculus book is thrown downward from the top of building-V, 168 ft high, at an angle of 60° with the horizontal. a. How far from the base of the building will the textbook land if its initial speed is 80 ft/sec? b. Will the textbook hit the cafeteria, if the cafeteria is 60 ft away from the base of the building-V on our campus? [No formulas from physics classes, please derive your own formulas, starting from ā(t)=< 0,-g > ]

College Physics
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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only do a if you don't want to do both.

### Problem 19

A calculus book is thrown downward from the top of Building-V, which is 168 feet high, at an angle of 60 degrees with the horizontal.

**a.** How far from the base of the building will the textbook land if its initial speed is 80 feet per second?

**b.** Will the textbook hit the cafeteria if the cafeteria is 60 feet away from the base of Building-V on our campus?

**Note:**
- No formulas from physics classes are allowed. Please derive your own formulas, starting from the given acceleration vector:  
  \[
  \vec{a}(t) = \langle 0, -g \rangle
  \]

**Instructions:** 
- Approach the problem by modeling the motion using basic kinematic principles and vector decomposition.
- Remember to resolve the initial velocity into horizontal and vertical components.
- Calculate the time of flight and determine the landing position of the textbook.
- Use logical reasoning to conclude whether the textbook will hit the cafeteria.

### Diagram Description

- The problem does not include a diagram. Visual learners might benefit from sketching a simple diagram showing the building, the angle of projection, and the trajectory of the textbook.
- Consider illustrating the horizontal distance from the base of the building and the location of the cafeteria.
Transcribed Image Text:### Problem 19 A calculus book is thrown downward from the top of Building-V, which is 168 feet high, at an angle of 60 degrees with the horizontal. **a.** How far from the base of the building will the textbook land if its initial speed is 80 feet per second? **b.** Will the textbook hit the cafeteria if the cafeteria is 60 feet away from the base of Building-V on our campus? **Note:** - No formulas from physics classes are allowed. Please derive your own formulas, starting from the given acceleration vector: \[ \vec{a}(t) = \langle 0, -g \rangle \] **Instructions:** - Approach the problem by modeling the motion using basic kinematic principles and vector decomposition. - Remember to resolve the initial velocity into horizontal and vertical components. - Calculate the time of flight and determine the landing position of the textbook. - Use logical reasoning to conclude whether the textbook will hit the cafeteria. ### Diagram Description - The problem does not include a diagram. Visual learners might benefit from sketching a simple diagram showing the building, the angle of projection, and the trajectory of the textbook. - Consider illustrating the horizontal distance from the base of the building and the location of the cafeteria.
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