С двух разных высот равных... - вопрос №803155

h1=v01t+gt1.^2/2

h2=v02t+gt2.^2/2

gt1.^2+2v0t1-2h1=0

t1=-v01+(v01.^2+2h1g).^0.5/g=(v0/g)((1+2gh1/v01.^2).^0.5-1)

t1=(v01/g)((1+2gh1/v01.^2).^0.5-1)=(5/10)((1+2*10*20/25).^0.5-1)=0.62 c

gt2.^2+2v02t2-2h2=0

t2=-v02+(v0.^2+2gh2).^0.5/g

t2=t1

-v02+(v02.^2+2h2g).^0.5/g=t1

v02.^2+2v02(v02.^2+2h2g).^0.5+v02.^2+2h2g=(t1g).^2

4v02.^2(v0.^2+2h2g)=((t1g).^2-2(v02.^2+h2g)).^2

4v02.^4+8h2v02.^2g= =(t1g).^4-4(t1g).^2(v02.^2+h2g)+4v02.^4+4v02.^2h2g+4(h2g).^2

(t1g).^4-4(t1gv02).^2-4t1.^2g.^3h2+4v02.^4+4v02.^2h2g+4(h2g).^2-4v02.^4-8h2v02.^2g=

=-4v02.^2g(h2+t1.^2g)+(t1g).^4-4t1.^2g.^3h2+4(h2g).^2

v02=(t1.^4g.^3-4t1.^2g.^2+4h2.^2g/4(h2+t1.^2g)).^0.5

v0=(g/4(h2+t1.^2g)).^0.5(t1.^4g.^2-4t1.^2g+4h2.^2).^0.5

v02=(10/4(30+0.62.^2*10)).^0.5(0.62.^4*100-40*0.62.^2+4*900).^0.5=16.31

v02=16.31 м/с