Груша масою 200 г висить на гілці на висоті І м. Яку потенціальну енергію
має груша? Яку максимальну кінетичну енергію набуде, коли почне падати на
землю? У який момент це відбудеться? Якою при цьому буде потенціальна енергія?

Падение
mgh=mv^2/2
v=корень(2gh)

удар
mv=(m+M)*u
u=m/(m+M)*v = m/(m+M)*корень(2gh)

сжатие пружины под действием силы
F=кх
k=F/x

сжатие пружины под действием движущегося груза на высоту H
(m+M)gH+(m+M)u^2/2=kH^2/2
kH^2/2 - (m+M)gH - (m+M)u^2/2 = 0
H^2 - 2(m+M)gH/k- (m+M)u^2/k = 0
H^2 - H*2*(m+M)*g*x/F- 2*g*h*m^2*x/(F*(m+M)) = 0
H^2 - H*2*(0,5+1)*9,8*0,01/9,8- 2*9,8*2*0,5^2*0,01/(9,8*(0,5+1)) = 0
H^2 - H* 0,03 - 0,006666667 = 0
H^2 - H* 3/100 - 2/300 = 0
D=9/10000+4*2/300= 0,027567
H=(3/100+ 0,166032)/2 = 0,098016 м ~ 10 см - это ответ
H=(3/100- 0,166032)/2 =  -0,06802  м  - лишний корень

Match the 2 parts of the sentences from paragraph of text 1.

Moldagulova Aliya Nurmukhambetovna was a sniper of the 54th sniper brigade. She was born on October 25, 1925 in a small village in Aktobe province. She was Kazakh. She lost her parents and lived in Almaty with her uncle. Since 1935, Aliya lived in orphanage No. 46 in Leningrad.

At the beginning of the war, she moved from Leningrad. She graduated from the 7th grade of high school in 1942. She studied at the Rybnisk Aviation Technical School. In 1943, she graduated from the school of snipers in Moscow. She was in the army since October 1943. Aliya Moldagulova was the brave and best sniper in the brigade. Aliya was one of the bravest soldiers of the Second World War. She was not afraid of enemies and made many efforts to win.