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A woman stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v0 = 20.5 m/s.The pebble leaves her hand at a height of h = 55.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand. Answer p

A woman stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v0 = 20.5 m/s.The pebble leaves her hand at a height of h = 55.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand. Answer p

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter3: Vectors
Section: Chapter Questions
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A woman stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v0 = 20.5 m/s.The pebble leaves her hand at a height of h = 55.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand. Answer parts a-f. 

### Projectile Motion of a Pebble In this lesson, we will analyze the projectile motion of a pebble that is thrown from a cliff. We'll determine the initial conditions, velocity components, position equations, time to impact, and the speed and angle of impact upon landing. #### Diagram Explanation: The given diagram shows a pebble being projected from the edge of a cliff with an initial velocity \( v_0 \). The pebble is launched at an angle \( \alpha \) to the horizontal. The initial height of the pebble above the ground is \( h \). The diagram includes: - A vertical coordinate (y-axis) denoted \( y \). - A horizontal coordinate (x-axis) denoted \( x \). - The initial launch angle \( \alpha \). - The initial velocity vector \( v_0 \). - Two components of the velocity: \( v_{0x} \) (horizontal) and \( v_{0y} \) (vertical). - The acceleration due to gravity, \( g \), acting downwards. ### Tasks: **(a) Initial Position Coordinates (Enter your answers in m):** - \( x_0 = \_\_\_\_ \ m \) - \( y_0 = \_\_\_\_ \ m \) **(b) Components of the Initial Velocity (Enter your answers in m/s):** - \( v_{0x} = \_\_\_\_ \ m/s \) - \( v_{0y} = \_\_\_\_ \ m/s \) **(c) Equations for the x- and y-components of the Velocity with Time:** - \( v_x = \_\_\_\_ \ m/s \) - \( v_y = \_\_\_\_ \ m/s \) **(d) Equations for the Position of the Pebble with Time using the Coordinates in the Figure:** - \( x = \_\_\_\_ \ m \) - \( y = \_\_\_\_ \ m \) **(e) Time to Impact:** - How long \( (t) \) after being released does the pebble strike the ground below the cliff? - \( t = \_\_\_\_ \ s \) **(f) Speed and Angle of Impact:** - At what speed \( (v_f) \) and angle of impact \( (\theta) \) in degrees clockwise from the \( +x
Transcribed Image Text:### Projectile Motion of a Pebble In this lesson, we will analyze the projectile motion of a pebble that is thrown from a cliff. We'll determine the initial conditions, velocity components, position equations, time to impact, and the speed and angle of impact upon landing. #### Diagram Explanation: The given diagram shows a pebble being projected from the edge of a cliff with an initial velocity \( v_0 \). The pebble is launched at an angle \( \alpha \) to the horizontal. The initial height of the pebble above the ground is \( h \). The diagram includes: - A vertical coordinate (y-axis) denoted \( y \). - A horizontal coordinate (x-axis) denoted \( x \). - The initial launch angle \( \alpha \). - The initial velocity vector \( v_0 \). - Two components of the velocity: \( v_{0x} \) (horizontal) and \( v_{0y} \) (vertical). - The acceleration due to gravity, \( g \), acting downwards. ### Tasks: **(a) Initial Position Coordinates (Enter your answers in m):** - \( x_0 = \_\_\_\_ \ m \) - \( y_0 = \_\_\_\_ \ m \) **(b) Components of the Initial Velocity (Enter your answers in m/s):** - \( v_{0x} = \_\_\_\_ \ m/s \) - \( v_{0y} = \_\_\_\_ \ m/s \) **(c) Equations for the x- and y-components of the Velocity with Time:** - \( v_x = \_\_\_\_ \ m/s \) - \( v_y = \_\_\_\_ \ m/s \) **(d) Equations for the Position of the Pebble with Time using the Coordinates in the Figure:** - \( x = \_\_\_\_ \ m \) - \( y = \_\_\_\_ \ m \) **(e) Time to Impact:** - How long \( (t) \) after being released does the pebble strike the ground below the cliff? - \( t = \_\_\_\_ \ s \) **(f) Speed and Angle of Impact:** - At what speed \( (v_f) \) and angle of impact \( (\theta) \) in degrees clockwise from the \( +x
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