A projectile is fired from a platform that is moving horizontally with velocity V = (V, 0, 0). The initial velocity of the projectile relative to the platform is u = (U₁, U₂, 0). Show that the range on a horizontal plane through the platform is 2Vu sin 20 +- sin 0, (1) 9 where u = √√√² + u² and 0 is the angle of projection (0 ≤ 0 ≤ ). Determine the value of that makes R a maximum, and calculate Rmax in terms of u, V and g. R(0) : ² sin = 9

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
Section: Chapter Questions
Problem 5CQ: Suppose you add two vectors A and B . What relative direction between them produces the resultant...
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A projectile is fired from a platform that is moving horizontally with velocity
V =
(V, 0, 0). The initial velocity of the projectile relative to the platform is
u = (U₁, U₂, 0). Show that the range on a horizontal plane through the platform is
u²
R(6) = sin
2Vu
sin 20 +- sin 0,
(1)
9
9
where u = √√√u?+ u² and 0 is the angle of projection (0 ≤ 0 ≤ ). Determine the
value of that makes R a maximum, and calculate Rmax in terms of u, V and g.
Transcribed Image Text:A projectile is fired from a platform that is moving horizontally with velocity V = (V, 0, 0). The initial velocity of the projectile relative to the platform is u = (U₁, U₂, 0). Show that the range on a horizontal plane through the platform is u² R(6) = sin 2Vu sin 20 +- sin 0, (1) 9 9 where u = √√√u?+ u² and 0 is the angle of projection (0 ≤ 0 ≤ ). Determine the value of that makes R a maximum, and calculate Rmax in terms of u, V and g.
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