Q. 45 Most geologists believe that the... [FREE SOLUTION]

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Chapter 11: Q. 45 (page 289)

Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 2.0 km and a mass of $1.0 脳 10^{13} k g$ hits the earth $(6.0 脳 10^{24} k g)$ with an impact speed of $4.0 脳 10^{4} m / s$ .
a. What is the earth鈥檚 recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.)
b. What percentage is this of the earth鈥檚 speed around the sun? The earth orbits the sun at a distance of $1.5 脳 10^{11} m$ .

Short Answer

Expert verified

Part (a). The earth鈥檚 recoil speed after collision is $6.67 脳 10^{- 8} m / s$

Part (b). Percentage of the recoil speed with the speed of the earth around sun is $2.23 脳 10^{- 10} %$

Step by step solution

Step 1. Given Information is:Diameter of the asteroid = 2 kmMass of the asteroid = 1.0×1013kgMass of the earth = 6.0×1024kgImpact speed = 4.0×104m/sEarth orbits the sun at a distance of 1.5×1011m

We need to find out :

a) The earth鈥檚 recoil speed after collision

b) Comparison of it with earth's speed around the sun.

Part (a). Step 1Using Law of conservation of Momentum.

$p_{a s t e r o i d} = p_{e a r t h} m_{a s t e r o i d} v_{a s t e r o i d} = m_{E a r t h} v_{E a r t h} (1 脳 10^{13} k g) (4 脳 10^{4} m / s) = (6 脳 10^{24} k g) v_{E a r t h} v_{E a r t h} = \frac{4 脳 10^{17} k g m / s}{6 脳 10^{24} k g} = 6.67 脳 10^{- 8} m / s$

Part (b). Step 1Calculating earth's speed around the sun.

We know that,

$v = \frac{2 蟺}{T} r T i s t h e t i m e p e r i o d o f e a r t h a r o u n d s u n t h a t i s, T = 365 d a y s = 365 脳 24 脳 3600 s e c o n d s = 31.536 脳 10^{6} s P u t t i n g v a l u e s, V_{e a r t h - S u n} = \frac{2 蟺}{31.536 脳 10^{6}} 脳 (1.5 脳 10^{11} m) V_{e a r t h - S u n} = 3 脳 10^{4} m / s P e r c e n t a g e o f r e c o i l s p e e d w i t h t h e s p e e d o f t h e e a r t h a r o u n d s u n i s : % = \frac{V_{e a r t h}}{V_{e a r t h - S u n}} \frac{6.67 脳 10^{- 8} m / s}{3 脳 10^{4} m / s} 脳 100 = 2.23 脳 10^{- 10} %$

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Short Answer

Step by step solution

Step 1. Given Information is:Diameter of the asteroid = 2 kmMass of the asteroid = 1.0×1013kgMass of the earth = 6.0×1024kgImpact speed = 4.0×104m/sEarth orbits the sun at a distance of 1.5×1011m

Part (a). Step 1Using Law of conservation of Momentum.

Part (b). Step 1Calculating earth's speed around the sun.

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