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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 k is given by the formula

k = 12 ρ C D A

where ρ is the density of the atmosphere, A is the frontal area of the object, and CD 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 CD = 0.5. The frontal area of the bowling ball is A = πr 2 where r is the radius. We will use ρ = 1.225kg/m3 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.

Grade:12th pass

2 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years 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
908 Points
3 years 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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