Explanation Given data: The acorn falls on a person’s head who is sitting on the deck of a house. Formula used: Write the kinematic equation of motion considering that the acceleration of an object remains constant during its motion. v 2 = u 2 + 2 a s Here v denotes final velocity, u denotes initial velocity, a denotes acceleration, and s denotes the displacement. From newton’s second law of motion, the net force acting on a body is: F = m a Here, m is the mass and a is the acceleration. Explanation: Consider the mass of the acorn to be 2 gram , or 0.002 kg and the distance covered by the acorn to be 20 m . The acorn falls from a condition of rest. Write the kinematic equation of motion during the motion from the tree to the person’s head and considering that the acceleration of the acorn remains constant during the motion. v 1 y 2 = v 01 y 2 + 2 g ( y 1 − y 0 1 ) Here, v 1 y denotes the final velocity with which it lands on the head, v 01 y denotes the initial velocity from the tree, g denotes acceleration due to gravity, and ( y 1 − y 01 ) denotes the vertical displacement of the acorn from tree to the head. Substitute, the values: 0 m/s for v 01 y , 9.8 m/s for g , and 20 m for ( y 1 − y 01 ) . v 1 y 2 = ( 0 m/s ) 2 + 2 ( 9.8 m/s 2 ) ( 20 m ) = 392 ( m/s ) 2 v 1 y = 19.79 m/s ≈ 19.8 m/s Therefore, the acorn drops with the velocity of 19.8 m/s . Consider that the acorn sinks 0.5 cm into the head. Again, for the motion during which the acorn sinks into the person’s head, write the third kinematic equation of motion considering the acceleration to be constant. v 2 y 2 = v 02 y 2 + 2 a 2 y ( y 2 − y 02 ) Here, v 2 y denotes the final velocity after dropping on the head, v 02 y denotes the initial velocity with which it sinks into the head, a 2 y denotes acceleration during the sinking, and ( y 2 − y 02 ) denotes the vertical displacement inside the head

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Author: ETKINA

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Chapter 3, Problem 46GP

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Whether an acorn falling from an oak tree will hurt a person. Consider the necessary details required in the solution.

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Chapter 3, Problem 45GP

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Whether an acorn falling from an oak tree will hurt a person. Consider the necessary details required in the solution.

Solution Summary: The author analyzes the kinematic equation of motion of an acorn falling from an oak tree.

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