A physics student performed a projectile experiment. She mentioned that as the initial angle of the projectile increases from 0 to 450, the range also increases (claim 1). Maximum range is attained at 450 (claim 2). As the initial angle increases above 450, the range of the projectile decreases (claim 3). She was able to verify the first claim in her experiment. Your task is to prove claim 1, 2 and 3 mathematically.

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
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Problem 29P: A delivery man starts at the post office, chives 40 km north, then 20 km west, then 60 km northeast,...
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A physics student performed a projectile experiment. She mentioned that as the initial angle of the projectile increases from 0 to 450, the range also increases (claim 1). Maximum range is attained at 450 (claim 2). As the initial angle increases above 450, the range of the projectile decreases (claim 3). She was able to verify the first claim in her experiment. Your task is to prove claim 1, 2 and 3 mathematically.
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