If we ignore air vesistance, then the range RO) of 'a ves pect to the X axis base ball hit at an angle e with and with initial velocity o is gien by RO) = (vos°sin (20) for Oso < where 1 is afceterat ion due to gravity. a) if Vo =50 cmrs) and ŷ =9.8(m/s?], then b) Detevenine those values of o for which R'C@)> o
If we ignore air vesistance, then the range RO) of 'a ves pect to the X axis base ball hit at an angle e with and with initial velocity o is gien by RO) = (vos°sin (20) for Oso < where 1 is afceterat ion due to gravity. a) if Vo =50 cmrs) and ŷ =9.8(m/s?], then b) Detevenine those values of o for which R'C@)> o
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The image contains an explanation and mathematical problem regarding the physics of projectile motion, specifically the range of a baseball hit at an angle θ, with an initial velocity v₀. Here's a detailed transcription:
---
**Projectile Motion: Range Calculation**
If we ignore air resistance, the range \( R(\theta) \) of a baseball hit at an angle \( \theta \) with respect to the x-axis and with initial velocity \( v_0 \) is given by:
\[ R(\theta) = \frac{1}{g}(v_0)^2 \sin(2\theta) \quad \text{for} \quad 0 \leq \theta < \frac{\pi}{2} \]
where \( g \) is the acceleration due to gravity.
### Problem:
a) If \( v_0 = 50 \, \text{m/s} \) and \( g = 9.8 \, \text{m/s}^2 \), then calculate:
\[ R'\left(\frac{\pi}{4}\right) \approx \, ? \]
b) Determine those values of \( \theta \) for which \( R'(\theta) > 0 \).
\[ \underline{\qquad\qquad} \leq \theta < \underline{\qquad\qquad} \, ? \]
---
This problem asks you to find the derivative of the range function at a specific angle and determine the interval for positive derivative values of the range function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f805aea-efd1-4603-9b0d-77a77b2a0177%2F7bb2820f-044b-42c5-97d7-db73780b6cd5%2Fsi4ddql_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains an explanation and mathematical problem regarding the physics of projectile motion, specifically the range of a baseball hit at an angle θ, with an initial velocity v₀. Here's a detailed transcription:
---
**Projectile Motion: Range Calculation**
If we ignore air resistance, the range \( R(\theta) \) of a baseball hit at an angle \( \theta \) with respect to the x-axis and with initial velocity \( v_0 \) is given by:
\[ R(\theta) = \frac{1}{g}(v_0)^2 \sin(2\theta) \quad \text{for} \quad 0 \leq \theta < \frac{\pi}{2} \]
where \( g \) is the acceleration due to gravity.
### Problem:
a) If \( v_0 = 50 \, \text{m/s} \) and \( g = 9.8 \, \text{m/s}^2 \), then calculate:
\[ R'\left(\frac{\pi}{4}\right) \approx \, ? \]
b) Determine those values of \( \theta \) for which \( R'(\theta) > 0 \).
\[ \underline{\qquad\qquad} \leq \theta < \underline{\qquad\qquad} \, ? \]
---
This problem asks you to find the derivative of the range function at a specific angle and determine the interval for positive derivative values of the range function.
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