Learning Goal: A rock thrown with speed 8.50 m/s and launch angle 30.0° (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s² for the free-fall acceleration.

Principles of Physics: A Calculus-Based Text
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Author:Raymond A. Serway, John W. Jewett
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Chapter3: Motion In Two Dimensions
Section: Chapter Questions
Problem 4OQ: Entering his dorm room, a student tosses his book bag to the right and upward at an angle of 45 with...
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Part C: Find the height yi from which the rock was launched. Express your answer in meters to three significant figures.
Learning Goal:
A rock thrown with speed 8.50 m/s and launch angle 30.0° (above the horizontal)
travels a horizontal distance of d = 19.0 m before hitting the ground. From what
height was the rock thrown? Use the value g = 9.800 m/s² for the free-fall
acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle, the initial velocity
components are vix
vocos and viy
vosine.
=
=
SOLVE: The acceleration is known: ax = 0 and
ay -g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are
=
Horizontal
xf = X₁ + V₁x At
Vfx = Vix constant
-
Vertical
Yf = Yi +ViyAt — — 9(At)²,
Vfy = Viy-gat
At is the same for the horizontal and vertical components of the motion. Find At from one component, and then use that value for the other component.
REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question.
Model
Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly.
Transcribed Image Text:Learning Goal: A rock thrown with speed 8.50 m/s and launch angle 30.0° (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s² for the free-fall acceleration. PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model. VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle, the initial velocity components are vix vocos and viy vosine. = = SOLVE: The acceleration is known: ax = 0 and ay -g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are = Horizontal xf = X₁ + V₁x At Vfx = Vix constant - Vertical Yf = Yi +ViyAt — — 9(At)², Vfy = Viy-gat At is the same for the horizontal and vertical components of the motion. Find At from one component, and then use that value for the other component. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Model Start by making simplifying assumptions: Model the rock as a particle in free fall. You can ignore air resistance because the rock is a relatively heavy object moving relatively slowly.
Part A
Which diagram represents an accurate sketch of the rock's trajectory?
► View Available Hint(s)
Submit
✓ Correct
Part B
a
Previous Answers
Submit
10
Correct
Uf
As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile's acceleration, ay, is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right.
Where you choose your origin doesn't change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest?
Previous Answers
U₂
At the peak of the trajectory
At the point where the rock strikes the ground
At the point where the rock is released
At ground level below the point where the rock is launched
O At ground level below the peak of the trajectory
U₂
Transcribed Image Text:Part A Which diagram represents an accurate sketch of the rock's trajectory? ► View Available Hint(s) Submit ✓ Correct Part B a Previous Answers Submit 10 Correct Uf As stated in the strategy, choose a coordinate system where the x axis is horizontal and the y axis is vertical. Note that in the strategy, the y component of the projectile's acceleration, ay, is taken to be negative. This implies that the positive y axis is upward. Use the same convention for your y axis, and take the positive x axis to be to the right. Where you choose your origin doesn't change the answer to the question, but choosing an origin can make a problem easier to solve (even if only a bit). Usually it is nice if the majority of the quantities you are given and the quantity you are trying to solve for take positive values relative to your chosen origin. Given this goal, what location for the origin of the coordinate system would make this problem easiest? Previous Answers U₂ At the peak of the trajectory At the point where the rock strikes the ground At the point where the rock is released At ground level below the point where the rock is launched O At ground level below the peak of the trajectory U₂
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