Chapter 7, Problem 65GP

Solution

a.

The change in speed of the space capsule.

  $V=0.194$ m/sec

Given information:

Mass of astronaut is 140 kg.

Speed acquired by astronaut is 2.50 m/sec

Mass of capsule is 1800kg.

Formula used:

  ${(mv+MV)}_i={(mv+MV)}_f$ here m and M are the masses of astronaut and capsules respectively. v and V are the velocity of astronaut and capsule. Subscript i and f denotes initial and final.

Calculation:

Initially the astronaut and capsule are at rest so

  ${\left(mv+MV\right)}_i=0$

Hence ${(mv+MV)}_f=0$

  $140\times 2.5+1800\times V=0$

  $V=-\frac{140\times 2.5}{1800}=0.194$ m/sec

b.

The average force exerted on the astronaut by the space capsule.

  $F=875N$

Given information:

Mass of astronaut is 140 kg.

Speed acquired by astronaut is 2.50 m/sec

Mass of capsule is 1800kg.

Formula used:

  $F=\frac{mV}{t}$

Calculation:

Substituting the values,

  $F=\frac{140\times 2.5}{0.40}=875N$