In the Marvel comic series X-Men, Colossus would sometimes throw Wolverine toward an enemy in what was called a fastball special. Suppose Colossus throws Wolverine at an angle of θ = 31.5° with respect to the ground (see figure below). Wolverine is d = 2.08 m above the ground when he is released, and he leaves Colossus's hands with a speed of vi = 18.2 m/s. (a) Using conservation of energy and the components of the initial velocity, find the maximum height attained by Wolverine during the flight. _____m (b) Using conservation of energy, what is Wolverine's speed the instant before he hits the ground? ______ m/s

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Chapter1: Units, Trigonometry. And Vectors
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In the Marvel comic series X-Men, Colossus would sometimes throw Wolverine toward an enemy in what was called a fastball special. Suppose Colossus throws Wolverine at an angle of θ = 31.5° with respect to the ground (see figure below). Wolverine is d = 2.08 m above the ground when he is released, and he leaves Colossus's hands with a speed of vi = 18.2 m/s.

(a) Using conservation of energy and the components of the initial velocity, find the maximum height attained by Wolverine during the flight. _____m

(b) Using conservation of energy, what is Wolverine's speed the instant before he hits the ground? ______ m/s

The image depicts a person launching another person into the air at an angle \(\theta\) with an initial velocity \(v_i\). The first person is standing on the ground and throws the second person upwards. The second person travels along a projectile path. The vertical distance from the ground to the horizontal plane where the initial velocity vector originates is labeled \(d\).

**Explanation:**

- **Initial Velocity (\(v_i\))**: Represented by an orange arrow, indicating the direction and magnitude at which the second person is launched.
  
- **Angle of Launch (\(\theta\))**: The angle between the initial velocity vector and the horizontal plane.
  
- **Vertical Distance (\(d\))**: The height difference from the launch position to the ground.

This diagram illustrates the basic principles of projectile motion, where an object is thrown into the air and moves under the influence of gravity alone. Key concepts include the trajectory path, initial speed, launch angle, and varying height. This information is relevant for understanding the mechanics behind projectile motion, often encountered in physics problems.
Transcribed Image Text:The image depicts a person launching another person into the air at an angle \(\theta\) with an initial velocity \(v_i\). The first person is standing on the ground and throws the second person upwards. The second person travels along a projectile path. The vertical distance from the ground to the horizontal plane where the initial velocity vector originates is labeled \(d\). **Explanation:** - **Initial Velocity (\(v_i\))**: Represented by an orange arrow, indicating the direction and magnitude at which the second person is launched. - **Angle of Launch (\(\theta\))**: The angle between the initial velocity vector and the horizontal plane. - **Vertical Distance (\(d\))**: The height difference from the launch position to the ground. This diagram illustrates the basic principles of projectile motion, where an object is thrown into the air and moves under the influence of gravity alone. Key concepts include the trajectory path, initial speed, launch angle, and varying height. This information is relevant for understanding the mechanics behind projectile motion, often encountered in physics problems.
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