Answered: A stone is thrown from the top of a…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A stone is thrown from the top of a building upward at an angle of 26.0° to the horizontal with an initial speed of 19.1 m/s as shown in the figure. The height of the building is 45.0 m.

The following questions present a twist on the scenario above to test your understanding.

Suppose another stone is thrown horizontally from the same building. If it strikes the ground 65 m away, find the following values.

a. Time of flight

________ s

b. Initial speed

________ m/s

c. Speed and angle with respect to the horizontal of the velocity vector at impact

________ m/s

________ °

If the stone were thrown harder, and left with 1.5 times the initial speed, you might expect it to go further, but how exactly does that happen?

d. Throwing the stone horizontally at 1.5 times the previous speed multiplies the time to reach the ground by what factor?

________

e. The horizontal component of the velocity is multiplied by what factor?

________

f. How many times farther does the stone land from the building?

________

The following questions present a twist on the scenario above to test your understanding.

Suppose another stone is thrown horizontally from the same building. If it strikes the ground 65 m away, find the following values.

(a) time of flight
[______] s

(b) initial speed
[______] m/s

(c) speed and angle with respect to the horizontal of the velocity vector at impact
[______] m/s
[______] °

If the stone were thrown harder, and left with 1.5 times the initial speed, you might expect it to go farther, but how exactly does that happen?

(d) Throwing the stone horizontally at 1.5 times the previous speed multiplies the time to reach the ground by what factor?
[______]

(e) The horizontal component of the velocity is multiplied by what factor?
[______]

(f) How many times farther does the stone land from the building?
[______]

### Description

The image is a diagram depicting a projectile motion scenario involving an object launched from the top of a building.

#### Key Elements:

1. **Building**:
- The building is drawn with a brick exterior and has multiple windows.
- The height of the building is labeled as 45.0 meters.

2. **Person and Launch Point**:
- A person is standing on top of the building, marked as the coordinate origin `(0, 0)`.
- The initial velocity of the projectile is indicated by an arrow labeled `vi`, launched at an angle `θi` from the horizontal axis `x`.

3. **Projectile Path**:
- The path of the projectile is a dashed parabolic arc starting from the launch point at the top of the building and ending on the ground.
- The projectile lands at an undefined horizontal distance `xf` from the base of the building.

4. **Axes and Coordinates**:
- The horizontal axis is labeled `x`.
- The vertical axis is labeled `y`.
- The final coordinates of the projectile when it reaches the ground level are indicated as `(xf, yf)`, where `yf = -45.0 m`.

5. **Labels**:
- The initial launch angle is denoted as `θi`.
- The question mark indicates that `xf` is an unknown value to be determined in this scenario.

This diagram serves to illustrate the basic principles of projectile motion, such as the effects of initial velocity, angle of launch, and the influence of gravity as the projectile moves from a high point to a lower point.

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