The range R and the maximum height H of a projectile fired at an inclination 0 to the horizontal with initial speed vo are given by vsin (20) v (sin 0² R(0) = and H(0) = where g 32.2 feet per second per second is the acceleration due to gravity. Find the range and maximum height of a projectile fired at an angle of 45° to the horizontal with an initial speed of 230 feet per second. g 2g R= (Round to two decimal places as needed.). H= (Round to two decimal places as needed.) V=Initial speed Height, H Range, R- H

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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The text discusses the range \( R \) and maximum height \( H \) of a projectile fired at an inclination \( \theta \) to the horizontal with an initial speed \( v_0 \). The formulas provided are:

\[ R(\theta) = \frac{v_0^2 \sin(2\theta)}{g} \]

\[ H(\theta) = \frac{v_0^2 (\sin \theta)^2}{2g} \]

where \( g \approx 32.2 \) feet per second squared is the acceleration due to gravity.

The task is to find the range and maximum height of a projectile fired at an angle of \( 45^\circ \) to the horizontal with an initial speed of 230 feet per second.

Below these equations is a diagram illustrating the trajectory of a projectile. The diagram shows:

- A projectile being fired with an initial speed \( v_0 \).
- The angle \( \theta \), the height \( H \), and the range \( R \).
- The path is a parabolic arc, demonstrating how the projectile reaches a maximum height before descending.

There are fields for entering values:

- **R =** [Input Box for Range with unit dropdown]
  - Instruction: (Round to two decimal places as needed.)

- **H =** [Input Box for Height with unit dropdown]
  - Instruction: (Round to two decimal places as needed.)
Transcribed Image Text:The text discusses the range \( R \) and maximum height \( H \) of a projectile fired at an inclination \( \theta \) to the horizontal with an initial speed \( v_0 \). The formulas provided are: \[ R(\theta) = \frac{v_0^2 \sin(2\theta)}{g} \] \[ H(\theta) = \frac{v_0^2 (\sin \theta)^2}{2g} \] where \( g \approx 32.2 \) feet per second squared is the acceleration due to gravity. The task is to find the range and maximum height of a projectile fired at an angle of \( 45^\circ \) to the horizontal with an initial speed of 230 feet per second. Below these equations is a diagram illustrating the trajectory of a projectile. The diagram shows: - A projectile being fired with an initial speed \( v_0 \). - The angle \( \theta \), the height \( H \), and the range \( R \). - The path is a parabolic arc, demonstrating how the projectile reaches a maximum height before descending. There are fields for entering values: - **R =** [Input Box for Range with unit dropdown] - Instruction: (Round to two decimal places as needed.) - **H =** [Input Box for Height with unit dropdown] - Instruction: (Round to two decimal places as needed.)
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