4.4 Failed rocket . An instrument-carrying rocket accidentally explodes at the top of), its trajectory. The horizontal distance between the launch point and the point of explosion is L. The rocket breaks into two pieces that fly apart horizontally. The larger piece has three times the mass, of the smaller piece. To the surprise of the scientist in charge, the smaller piece returns to Earth at the launching station. How far away does the larger piece land? Neglect air resistance and effects due to the Earth's curvature.

{-~ Ce « ft"r t!J-j:~1L.$..s /CLYlcl~ /u./<_

~t.fjv( X )o +-

\ '\. ) 0 c. J-t'&v\. W l-:« r JL l (J C a.:I-iVV1

c ."fV1." t Gl ~dS r e Irk:.t:'V( w h..t.", e I CfrJ.{ ftt; ItA 1-4}1?J C I\._ Pit c e 14t\d..s

3, ..._...,~L >< - 't

~LX' ::.. 3 r 'J" l

4;5 Acrobat and monkey i A circus acrobat of mass M leaps straight up with initial velocity

Vo from a trampoline. As he rises up, he takes a trained monkey of mass m off a perch at a height h above the trampoline.

What is the maximum .height attained by the pair?

~ k /N ""..J 1(.s It' o.f «: c VO bk I- . w. ~ Cf Y'Ab 5 ) LLI ,/ ~ fA..J2 Wl.. t/y'/ (~ v: :. 1(,2 ~2_jk

tJ~t-tr

V18M-rM ~ -h~d _s~d

C-t f!-f~r ~ J r:a: bJ

1<"/I\..L~Jlc. s ~y

() ']._ ....

M 2.V/ J_ 2:; M rA '" ~- 1:J 1M2_. ~ ':- "-------------_.-._.----_ ..._._.. _-----

?--c; (l1 -}- Yl-'l) 'L

4:6 Emergency landing .t A light plane weighing 2500 Ib makes an emergency landing on> a short runway. With its engine off, it lands on the runway at 120 ft/s. A hook on the plane snags a cable attached to a 250-lb sandbag and drags the sandbag along. If the coefficient of fric­ tion between the sandbag and the runway is 0.4, and if the plane's brakes give an additional retarding force of 300 lb, how far does

. the plane go before it comes to a stop?

I~ C()/~ ~ S c:t JJv:;/h':J ~ L~ JVe?j.,4/; .$~ lel$ Md:;'~(J~

-(~~ bd/~_ 9/4bJ -- :25 tHJ +- 2ff0 ~ /tJi-% :::::. br'tPct )://1 ~ c: 3CJ6 /65

3.2:ff..__ ( if a o /b~) _----"'------2 --;:: (f ) /:; 5'

~ '!,(PS -f7s7.;

v '7_ ~ ~ z, .:J- 2- tA. . ci.: () ~ (! 07) '1 - 2 (L/ ' to 5) t{_

/092_ 2CuJ'~~)

rA -

4.8 Jumper A 50 kg woman jumps straight into the air, rising 0.8 m from the 'ground. What impulse does she receive from the ground to attain

: ' \ .. this height?

lA -~ a~~ ~ ,.-

1<)m :: ~O

V '2..

'7/0 Z. - 2) J.._

v~ CJ :::-0 -~ 4_

z- ..... C,) -.. J.2-J /._

'1~J_s~ ~ ";::.Lp M1/ -rJ /;2._) t._M_(J

5CJ I~ [2, f, ~'~"t- ' o. 8 vtA. -,

(Ii g I~