Part 1) Warm-up: What is the angle that maximizes the range of a projectile if fired across a flat surface (see below) | Range Find the max range if the projectile speed is 3.0 m/s. a) Find the range of the projectile if it is fired at 20. degrees above the horizon. Write your answer as a numerical value. b) Find the range of the projectile if it is fired at an arbitrary angle ". Write your answer as an algebraic expression. c) Solve the equation for ", Range = 0. Write a brief statement explaining why those firing angles have a range of zero. Include a picture of the projectile's trajectory for these situations. d) Sketch a graph of Range as a function of below, dR e) For what value is the Range at a maximum? Solve this by taking the derivative do setting it equal to zero and solving for ".

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Chapter4: Motion In Two And Three Dimensions
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Part 1) Warm-up: What is the angle that maximizes the range of a projectile if fired across a flat surface (see below)
| Range
Find the max range if the projectile speed is 3.0 m/s.
a) Find the range of the projectile if it is fired at 20. degrees above the horizon. Write your answer as a numerical value.
b) Find the range of the projectile if it is fired at an arbitrary angle ". Write your answer as an algebraic expression.
c) Solve the equation for , Range = 0. Write a brief statement explaining why those firing angles have a range of zero.
Include a picture of the projectile's trajectory for these situations.
d) Sketch a graph of Range as a function of below.
dR
e) For what value
is the Range at a maximum? Solve this by taking the derivative de
", setting it equal to zero and
solving for 6.
f) Find the range of the projectile if it is fired at 20. degrees above the horizon and is launched off a table whose height is
2.0 meters.
g) Repeat steps b-e above but for an arbitrary angle and arbitrary height 'h' compare your results with data collected
in lab.
Transcribed Image Text:Part 1) Warm-up: What is the angle that maximizes the range of a projectile if fired across a flat surface (see below) | Range Find the max range if the projectile speed is 3.0 m/s. a) Find the range of the projectile if it is fired at 20. degrees above the horizon. Write your answer as a numerical value. b) Find the range of the projectile if it is fired at an arbitrary angle ". Write your answer as an algebraic expression. c) Solve the equation for , Range = 0. Write a brief statement explaining why those firing angles have a range of zero. Include a picture of the projectile's trajectory for these situations. d) Sketch a graph of Range as a function of below. dR e) For what value is the Range at a maximum? Solve this by taking the derivative de ", setting it equal to zero and solving for 6. f) Find the range of the projectile if it is fired at 20. degrees above the horizon and is launched off a table whose height is 2.0 meters. g) Repeat steps b-e above but for an arbitrary angle and arbitrary height 'h' compare your results with data collected in lab.
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