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
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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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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![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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb53001b8-eebf-43c2-bee7-cb0ec77b1cc7%2F965a258a-90e7-4d2d-b149-81807b1bf465%2Fbgtooe_processed.png&w=3840&q=75)
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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Step 1: Equation for the horizontal range of the projectile motion:
VIEWStep 2: Finding the value of the horizontal range of the projectile motion:
VIEWStep 3: Equation for the maximum height reached by the projectile:
VIEWStep 4: Finding the value for the maximum height reached by the projectile:
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