Explanation Given data: The bird is dropped a vertical distance of 208 m in 3.0 s. Mass of the swallow ( m ) is 0.018 kg. The distance dived by the swallow ( Δ y ) is 208 m. Time taken by the swallow for its dive ( Δ t ) is 3.0 s. Cross-sectional area of the swallow ( A ) is 5.6 × 10 − 4 m 2 . Formula used: Refer to the equation (5.12) in the textbook, and modify the expression for drag force on the on the swallow when it’s diving as follows. D = 1 2 C D ρ A ( v y ) f 2 (1) Here, C D is the drag coefficient for the diving swallow, ρ is the density of the air, which is 1.2 kg m 3 at sea level, A is the cross-sectional area of the swallow, and ( v y ) f is the final speed of the swallow. Write the expression for final speed of the swallow by using kinematic equation as follows. ( v y ) f = ( v y ) i + a y Δ t (2) Here, ( v y ) i is the initial speed of the swallow, ( v y ) f is the final speed of the swallow, a y is the acceleration of the swallow. and Δ t is the acceleration duration (time taken by the swallow for its dive). Write the expression for distance travelled by the swallow in its dive by using kinematic equation as follows. Δ y = ( v y ) i Δ t + 1 2 a y ( Δ t ) 2 (3) Write the expression for apparent weight of the swallow for its downward dive as follows. w app = w − m a y (4) Here, w is the actual weight of the swallow. Write the expression for actual weight of the swallow (normal weight due to gravity of the earth) as follows. w = m g (5) Here, g is the acceleration due to gravity of the earth, which is 9.8 m s 2 . Explanation: Calculation of acceleration of the swallow ( a y ) : As the bird is dropped from the rest, the initial speed of the bird is considered as 0 m s . ( v y ) i = 0 m s Rearrange the expression in equation (3) to find the acceleration of the swallow as follows. a y = 2 [ Δ y − ( v y ) i Δ t ] ( Δ t ) 2 Substitute 208 m for Δ y , 0 m s for ( v y ) i , and 3.0 s for Δ t , a y = ( 2 ) [ 208 m − ( 0 m s ) ( 3.0 s ) ] ( 3.0 s ) 2 = 46.2223 m s 2 Calculation of final velocity of the swallows [ ( v y ) f ] : Substitute 0 m s for ( v y ) i , 46.2223 m s 2 for a y , and 3

4th Edition

ISBN: 9780134779218

Author: Knight

Publisher: PEARSON

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Chapter 5, Problem 68GP

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To find: The drag coefficient for the diving swallow.

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Chapter 5, Problem 67GP

Chapter 5, Problem 69GP

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