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)

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Chapter3: Motion Along A Straight Line
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Problem 113CP: The position of a particle moving along the x -axis varies with time according to x(t)=5.0t24.0t3 ....
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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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