Textbook Question
A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (b) At what time is it moving at 20.0 m/s downward?
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Ch 02: Motion Along a Straight Line
Chapter 2, Problem 2
A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (e) What are the magnitude and direction of the acceleration while the boulder is (i) moving upward? (ii) Moving downward? (iii) At the highest point?
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Identify the forces acting on the boulder throughout its motion. Since air resistance is ignored, the only force acting on the boulder is gravity, which always acts downward towards the center of the Earth.
Recall that acceleration due to gravity is constant near the Earth's surface and is approximately 9.8 m/s^2 downward. This value is denoted as 'g'.
(i) While the boulder is moving upward, it is slowing down due to the gravitational pull acting in the opposite direction of its motion. The acceleration is -9.8 m/s^2 (downward).
(ii) When the boulder is moving downward, it is speeding up under the influence of gravity. The acceleration remains constant at 9.8 m/s^2 (downward).
(iii) At the highest point of its trajectory, even though the velocity of the boulder is zero for an instant, the acceleration due to gravity still acts on it and remains 9.8 m/s^2 downward.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Acceleration due to Gravity
Acceleration due to gravity is a constant force acting on objects near the Earth's surface, typically denoted as 'g'. Its value is approximately 9.81 m/s² downward. This force influences the motion of the boulder both when it is moving upward and downward, regardless of its velocity.
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Acceleration Due to Gravity
Kinematics of Projectile Motion
Kinematics describes the motion of objects without considering the forces that cause the motion. In projectile motion, an object follows a parabolic trajectory under the influence of gravity. The boulder's upward and downward movements can be analyzed using kinematic equations, which relate displacement, velocity, acceleration, and time.
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Velocity and Direction
Velocity is a vector quantity that includes both speed and direction. As the boulder moves upward, its velocity decreases until it reaches zero at the highest point, where it then begins to descend. The direction of acceleration remains constant at downward throughout the boulder's flight, indicating that gravity is always acting to pull it back toward the Earth.
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Related Practice
Textbook Question
A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (c) When is the displacement of the boulder from its initial position zero?
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Textbook Question
A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (d) When is the velocity of the boulder zero?
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Textbook Question
An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 10-s interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Assume that the positive direction is to the right. (a) At the beginning of the interval, the astronaut is moving toward the right along the x-axis at 15.0 m/s, and at the end of the interval she is moving toward the right at 5.0 m/s. (b) At the beginning she is moving toward the left at 5.0 m/s, and at the end she is moving toward the left at 15.0 m/s. (c) At the beginning she is moving toward the right at 15.0 m/s, and at the end she is moving toward the left at 15.0 m/s.
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Textbook Question
At launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 161 km/h; at the end of the first 1.00 min, its speed is 1610 km/h. (a) What is the average acceleration (in m/s2) of the rocket (i) during the first 8.00 s and (ii) between 8.00 s and the end of the first 1.00 min?
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Textbook Question
A physics professor leaves her house and walks along the sidewalk toward campus. After 5 min it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.10. At which of the labeled points is her velocity (a) zero?
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