Q$4\_2.$ A ball is launched with an initial velocity of v$0=4\mathrm{.}5\frac{m}{s}$ from point $P$ at a $30$ sloped surface with an angle of $.$ The ball lands at point $B,$ which is $0\mathrm{.}6$ m higher than point $A.$ Determine the launch angle $$ of the ball, the impact velocity at $B(v_B),$ the angle $v_B$ makes with the horizontal and the duration of the flight. Also determine the radius of curvature of the path and the rate of change of the speed of the ball at point $C,$ where its trajectory makes an angle of $60$ with the negative x $-$axis. $g=9\mathrm{.}81\frac{m}{s^2}.$

S$4\_2.$ Bir top $P$ noktas$$ndan $v_0=4\mathrm{.}5\frac{m}{s}$ ba$$lang$$ h$$z$$ ve yatayla $$ a$$s$$ yapacak bi$$imde $30$ e$$imli bir y$$zeyden firlat$$liyor$.$ Top $A^{\text{'}}$ dan $0\mathrm{.}6$ m daha y$$ksek olan $B$ noktas$$na d$$yor$.$ Topun firlat$$lma a$$s$\text{'}$y$,B\text{'}$ye vurma h$$z$$n$(v_B),v_B$ 'nin yatayla yapt$$ a$$y$$ ve toplam u$$u$$ s$$resini belirleyiniz. Ayr$$ca y$$r$$ngenin negatif $x$ ekseniyle $60$ a$$ yapt$C$ noktas$$nda topun y$$r$$ngesinin e$$rilik yar$$ap$$ ile s$$ratin zamana ba$$l$$ de$$i$$imini de hesaplay$$n$$z$.g=9\mathrm{.}81\frac{m}{s^2}.$

$=70\mathrm{.}507,(v_B{)}_x=1\mathrm{.}502\frac{m}{s},(v_B{)}_y=-2\mathrm{.}488\frac{m}{s}$

$v_B$ 'nin yatayla yapt$$ a$$: $58\mathrm{.}88,$

C noktas$$nda te$$et do$$rultu $60$ lik a$$ yap$$yor$.$

C noktas$$ndada $=1\mathrm{.}839m,a_t=-8\mathrm{.}496\frac{m}{s^2}$

T$$rk$$e ve ka$$da $$ekilli $$z