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# c)The constant k is given by the formulak = 12 ρ C D Awhere 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.

## 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
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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