6.32 Part C The asteroid 243 Ida has a mass of about 4.0 × 1016 kg and an averag

Question

6.32 Part C The asteroid 243 Ida has a mass of about 4.0 × 1016 kg and an average radius of about 16 km (it's not spherical but you can assume it is) If you dropped a rock trom a height of 1.2 m on 243 Ida, how long would take to reach the ground? Express your answer to two significant figures and include the appropriate units t= 1 Value ls f you can jump 56 ean straight up on earth, how high could you jump on 243 da? (Assime the asteroid's gravity deesn't weaken signicanty distance of your jump ) Part D Units

Explanation / Answer

accelaration of the body is a = G*M/r^2

G is the universal gravitational constant

M is the mass of the asteroid

r is the radius of the asteroid = 16000 m

then a = G*M/r^2 = (6.67*10^-11*4*10^16)/(16000^2) = 0.0104 m/s^2

initial velocity is Vo = 0 m/sec

distance travelled is 1.2 m

then using kinematic equations

S = (Vo*t)+(0.5*a*t^2)

1.2 = (0*t)+(0.5*0.0104*t^2)

t = 15.2 sec

D) Hmax = Vo^2/(2*g)

0.56 = Vo^2/(2*9.8)

Vo = 3.31 m/sec

on asteroid is Hmax = Vo^2/(2*g) = 3.31/(2*0.0104)

Hmax = 159.13 m

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