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Vector Decomposition: A rocket hits the ground at an angle of 60 degrees from the horizontal at a speed of 300 m/s.

a) Draw the vector representing the rocket's impact and its components.
b) Calculate the horizontal and vertical components of the rocket's impact velocity.

A) Draw the vector representing the rocket's impact and its components.
B) Calculate the horizontal and vertical components of the rocket's impact velocity.

User Tadalendas
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1 Answer

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Final answer:

In Physics, the rocket impact's horizontal and vertical velocity components are calculated using trigonometry from the given angle of 60 degrees and speed of 300 m/s. The horizontal component is 150 m/s, while the vertical component is approximately 259.8 m/s.

Step-by-step explanation:

The question involves the concept of vector decomposition in projectile motion, part of Physics. To represent the rocket's impact, we need to draw a two-dimensional vector showing the impact direction and decompose it into horizontal (x) and vertical (y) components. This vector would make a 60-degree angle with the horizontal axis. The horizontal and vertical components of the velocity can be calculated using trigonometry:

  • Horizontal component: Vx = v × cos(θ)
  • Vertical component: Vy = v × sin(θ)

For the rocket's impact at a speed of 300 m/s and an angle of 60 degrees:

  • Vx = 300 m/s × cos(60°) = 300 m/s × 0.5 = 150 m/s
  • Vy = 300 m/s × sin(60°) = 300 m/s × √3/2 ≈ 259.8 m/s

The horizontal component of the rocket's impact velocity is 150 m/s, and the vertical component is approximately 259.8 m/s.

User Khoroshevj
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