Part C Find the height yi from which the rock was launched. Express your answer in meters to three significant figures. Learning Goal: To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 12.0 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 θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ. SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are Horizontalxf=xi+vixΔtvfx=vix=constantVerticalyf=yi+viyΔt−12g(Δt)2vfy=viy−gΔt, Δt is the same for the horizontal and vertical components of the motion. Find Δtfrom 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 C Find the height yi from which the rock was launched. Express your answer in meters to three significant figures. Learning Goal: To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 12.0 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 θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ. SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are Horizontalxf=xi+vixΔtvfx=vix=constantVerticalyf=yi+viyΔt−12g(Δt)2vfy=viy−gΔt, Δt is the same for the horizontal and vertical components of the motion. Find Δtfrom 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 C Find the height yi from which the rock was launched. Express your answer in meters to three significant figures. Learning Goal: To practice Problem-Solving Strategy 4.1 for projectile motion problems. A rock thrown with speed 12.0 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 θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ. SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are Horizontalxf=xi+vixΔtvfx=vix=constantVerticalyf=yi+viyΔt−12g(Δt)2vfy=viy−gΔt, Δt is the same for the horizontal and vertical components of the motion. Find Δtfrom 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.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 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.
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 θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of two-dimensional kinematics. The kinematic equations are
Δt is the same for the horizontal and vertical components of the motion. Find Δtfrom 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.
Study of objects in motion.
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