A4_solution_9th_edition corrected

4320 hA = 4300 km A

R = 6370 km

13.87 PROBLEM 13.85

km

Knowing that the velocity of an experimental space probe fired from the earth has a magnitude v A 32.32 32.5 Mm/h at point A, determine the velocity of the probe as it passes through point B.

vA

hB = 12 12700640 km

km

B vB

SOLUTION rA

hA  R

rA

10.69Mm Mm 10.67

rB

4.32Mm 6.37 4.3 Mm  +6.37 MmMm

hB  R

72.7 MmMm  6.37 MmMm 12.64 + 6.37

rB

19.07 Mm 19.01 Mm

At A,

vA TA

1 2 8978 m/s m  9028 2 VA

rA R

32.5 MMm/h m/h =9028 m/s 32.32 8978 m/s



 gR 2m rA

GMm rA

10.69 u 106 m 10.67

10.69 M Mm 10.67 m

6370 km

6

40.302 xu 10 40.752 106mm

6.37 u 106 m

9.81 m/s  6.37 u 10 m  10.69 u 10 m 10.67 2

VA

At B

rB

1 2 mvB ; VB 2



37.237 u 106 m  37.306

 gR 2m rB

GMm rB

9.81 m/s  6.37 u 10 m  19.01 u 10 m 19.07 6

2

m

6

6 20.939 u 10 m 20.874

40.302 u 106 m  37.306 37.237 u 106 m TB  VB ; 40.752

vB2

m

6 19.01 u 10 m 19.07

19.01 19.07 Mm Mm 2

TA  VA

2

6

TB

VB

6

1 2 20.939 u 106 m mvB  20.874 2

37.237 u 106  20.939 2 ª¬40.302 40.752 u 106  37.306 20.874 u 106 º¼

vB2 vB

6 2 2 48.01 u 10 m /s 48.64

6.929 u 103 m/s 6.9742

24.944 Mm/h 25.107

vB

25.1 Mm/h W 24.9

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