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c)The constant k is given by the formula k = 1 2 ρ C D A where ρ is the density of the atmosphere, A is the frontal area of the object, and C D is a dimensionless constant called the “drag coefficient” which measures how aerodynamic the object is. For instance, according to Wikipedia, the Tesla Model 3 has a drag coefficient of 0.23 and Usain Bolt has a drag coefficient of 1.2. In this question, we will consider a spherical bowling ball, for which we may assume the drag coefficient is C D = 0.5. The frontal area of the bowling ball is A = π r 2 where r is the radius. We will use ρ = 1.225kg/m 3 for the density of air. Calculate the constant k for a seven kilogram bowling ball with a diameter of 21.5cm. 2 (d) On the Earth, acceleration due to gravity is given by g = 9.81 m/s . If a bowling ball as in part (c) were dropped from the height of 2 kilometers, how long would it take to fall and what would its velocity be upon hitting the ground? Express your answer with at least three significant digits.

c)The constant is given by the formula

1ρ A

where ρ is the density of the atmosphere, is the frontal area of the object, and Cis a dimensionless constant called the “drag coefficient” which measures how aerodynamic the object is. For instance, according to Wikipedia, the Tesla Model 3 has a drag coefficient of 0.23 and Usain Bolt has a drag coefficient of 1.2. In this question, we will consider a spherical bowling ball, for which we may assume the drag coefficient is C0.5. The frontal area of the bowling ball is πwhere is the radius. We will use ρ 1.225kg/mfor the density of air.

Calculate the constant for a seven kilogram bowling ball with a diameter of 21.5cm. 2

(d) On the Earth, acceleration due to gravity is given by 9.81 m/s . If a bowling ball as in part (c) were dropped from the height of 2 kilometers, how long would it take to fall and what would its velocity be upon hitting the ground? Express your answer with at least three significant digits.

Grade:12th pass

2 Answers

Harshit Singh
askIITians Faculty 5963 Points
6 months ago
Dear Student

Here is solution to your query c
Please ask d in separate thread

Given diameter = 21.5 cm
radius = 10.75 cm
Area =πr^2 = 363.05 cm^2 = 0.0363 m^2
Drag coefficient = 0.5
ρ=1.225 kg/m^3
Putting all these values

k = 0.01111

Thanks
Yashraj
915 Points
6 months ago
  1. Practice previous year questions many times..
  2. Appear for a test series and analyse it properly (Giving 2–3 hours)
  3. Revise your notes multiple times till they enter your soul :)
  4. Find your strong points and chapters, work on them..
  5. Solve other people’s doubts. It makes your own concepts very clear

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