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For a projectile lunched with an initial velocity of v0 at an angle of θ (between 0 and 90o) . For what value of θ gives the highest maximum height? Solution  The components of v0 are expressed as follows: vinitial-x = v0cos(θ) vinitial-y = v0sin(θ)

For a projectile lunched with an initial velocity of v0 at an angle of θ (between 0 and 90o) . For what value of θ gives the highest maximum height? Solution  The components of v0 are expressed as follows: vinitial-x = v0cos(θ) vinitial-y = v0sin(θ)

College Physics
College Physics
11th Edition
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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For a projectile lunched with an initial velocity of v0 at an angle of θ (between 0 and 90o) . For what value of θ gives the highest maximum height?

Solution 

The components of v0 are expressed as follows:

vinitial-x = v0cos(θ)

vinitial-y = v0sin(θ)

The distance traveled by a projectile follows a uniform motion, meaning, velocity is constant from the start point until it reach the ground along the horizontal axis, so, the range R can be expressed as R = Vinitial-xt Substituting the initial velocity on the x-axis results to the following R = ( )t But, the time it takes a projectile to travel this distance is just twice of tmax-height by substitution, we obtain the following: R = x 2 x ( Re-arranging and then applying the trigonometric identity sin(2x) = 2sin(x)cos(x) we arrive at the expression for the range R as R = sin
Transcribed Image Text:The distance traveled by a projectile follows a uniform motion, meaning, velocity is constant from the start point until it reach the ground along the horizontal axis, so, the range R can be expressed as R = Vinitial-xt Substituting the initial velocity on the x-axis results to the following R = ( )t But, the time it takes a projectile to travel this distance is just twice of tmax-height by substitution, we obtain the following: R = x 2 x ( Re-arranging and then applying the trigonometric identity sin(2x) = 2sin(x)cos(x) we arrive at the expression for the range R as R = sin
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