Answer:
a). v3= 9.52 m/s
b). U= 637.98 J
Explanation:
[tex]m=62kg\\v1=6.5\frac{m}{s}\\ s=3.5m\\h=2.5m\\uk=0.300\\Wt=Wo+Wg=K2-K1[/tex]
The work of gravity is about the distance and the work in the force in the distance so
∑[tex]Fy=N-mg[/tex]
[tex]N=m*g\\N=62kg*9.8\frac{m}{s^{2} }=607.6N[/tex]
[tex]Fk=u*N\\Fk=0.30*607.6N\\Fk=182.68N[/tex]
[tex]Wo=Fk*d\\Wo=128.28N*3.5m\\Wo=637.98J[/tex]
Now calculated K1
[tex]K1=\frac{1}{2}*m*(v1)^{2}\\K1=\frac{1}{2}*62kg*(6.5\frac{m}{s})^{2}\\K1=1309.75N*m[/tex]
[tex]Wo+0=K2-K1\\637.98+0=\frac{1}{2}*m*(v2)^{2}-1309.75 N*m[/tex]
[tex]637=31*(v2)^{2}-1309.75\\(v2)^{2}= \frac{1946.75}{31}\\ v2=\sqrt{62.79 } \\v2=7.924 \frac{m}{s}[/tex]
[tex]K2=\frac{1}{2}*m*(v2)^{2}=\frac{1}{2}*62kg*(7.9\frac{m}{s})^{2} \\K2=1946.75[/tex]
[tex]Wg=m*g*h1\\Wg=62kg*9.8*2,5m\\Wg=1519J[/tex]
[tex]Wg=K3-K2\\1519=K3-1309.75J\\K3=2828.75J\\\frac{1}{2}*m*(v3)^{2} =2828.75J\\(v3)^{2} =91.25J\\v3=\sqrt{91.25} =9.552\frac{m}{s}[/tex]
