A cannon elevated at some angle ? (unknown) fires a shell with some initial speed v0 (unknown) that has a range R when fired over level ground (see Figure (a)). During a test fire, a shell explodes at the top of the trajectory into two unequal mass fragments. The shell explodes in such a manner that neither fragment experiences a change in momentum in the y direction. However, 28% of the shell (m2) continues onward and the other fragment (m1) falls straight down. Determine the distance D (in terms of R) that the forward moving fragment lands from the cannon (see Figure (b)).D = The image illustrates two scenarios of projectile motion: (a) without an explosion and (b) with an explosion.### Diagram (a): No Explosion- **Trajectory**: A dashed parabolic path shows the motion of the projectile.- **Initial Conditions**: The projectile is launched from a cannon at an initial velocity \( v_0 \) and an angle \( \theta \) above the horizontal.- **Parameters**: - The range \( R \) is the horizontal distance traveled by the projectile when there is no explosion.### Diagram (b): With Explosion- **Trajectory**: Similar to the first scenario, the motion is initially a parabolic path.- **Explosion**: - An explosion occurs at the peak of the trajectory denoted by an orange burst. - This explosion splits the projectile into two fragments, \( m_1 \) and \( m_2 \).- **Effects of Explosion**: - The explosion results in the components \( m_1 \) and \( m_2 \) following different paths after the explosion. - The distance \( D \) represents the horizontal distance traveled to the explosion site.Both graphs have the same coordinate axes labeled \( x \) (horizontal) and \( y \) (vertical). The cannon angle and initial velocity vector \( v_0 \) are depicted similarly in both diagrams.

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Description: A cannon elevated at some angle ? (unknown) fires a shell with some initial speed v0 (unknown) that has a range R when fired over level ground (see Figure (a)). During a test fire, a shell explodes at the top of the trajectory into two unequal mass f

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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 cannon elevated at some angle ? (unknown) fires a shell with some initial speed v₀ (unknown) that has a range R when fired over level ground (see Figure (a)). During a test fire, a shell explodes at the top of the trajectory into two unequal mass fragments. The shell explodes in such a manner that neither fragment experiences a change in momentum in the y direction. However, 28% of the shell (m₂) continues onward and the other fragment (m₁) falls straight down. Determine the distance D (in terms of R) that the forward moving fragment lands from the cannon (see Figure (b)).
D =

The image illustrates two scenarios of projectile motion: (a) without an explosion and (b) with an explosion.

### Diagram (a): No Explosion

- **Trajectory**: A dashed parabolic path shows the motion of the projectile.
- **Initial Conditions**: The projectile is launched from a cannon at an initial velocity \( v_0 \) and an angle \( \theta \) above the horizontal.
- **Parameters**:
- The range \( R \) is the horizontal distance traveled by the projectile when there is no explosion.

### Diagram (b): With Explosion

- **Trajectory**: Similar to the first scenario, the motion is initially a parabolic path.
- **Explosion**:
- An explosion occurs at the peak of the trajectory denoted by an orange burst.
- This explosion splits the projectile into two fragments, \( m_1 \) and \( m_2 \).
- **Effects of Explosion**:
- The explosion results in the components \( m_1 \) and \( m_2 \) following different paths after the explosion.
- The distance \( D \) represents the horizontal distance traveled to the explosion site.

Both graphs have the same coordinate axes labeled \( x \) (horizontal) and \( y \) (vertical). The cannon angle and initial velocity vector \( v_0 \) are depicted similarly in both diagrams.

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