Answer:
a.[tex]I=981.34 N*s[/tex]
b.[tex]v_f=3.96 m/s[/tex]
c.[tex]v_{f1}=3.63m/s[/tex]
d.[tex]y_f=0.673m[/tex]
Explanation:
Given: [tex]m=67kg[/tex], [tex]h=0.720m[/tex], [tex]0<t<0.80s[/tex]
a.
[tex]I=\int\limits^{t_1}_{t_2} {F(t)} \, dt[/tex]
[tex]F(t)=9200*t-11500t^2[/tex]
[tex]I=\int\limits^{0.8s}_{0s}{9200*t-11500*t^2} \, dt[/tex]
[tex]I=4600*t^2-3833.3*t^3|(0.80,0)[/tex]
[tex]I=2944-1962.66=981.35[/tex]
[tex]I=981.34 N*s[/tex]
b.
[tex]v_f^2=v_i^2+a*y'[/tex]
Starting from the rest
[tex]v_f^2=0+2*9.8m/s^2*0.80s[/tex]
[tex]v_f^2=15.68[/tex]
[tex]v_f=\sqrt{15.68m^2/s^2}=3.96 m/s[/tex]
c.
[tex]I_{total}=p_f[/tex]
[tex]I_1-m*g*d=m*v_{f1}-m*v_f[/tex]
[tex]981.34-67kg*9.8m/s^2*0.720=67.0kg*v_{f1}-67.0kg*(-3.96m/s)[/tex]
Solve to vf
[tex]v_{f1}=3.63m/s[/tex]
d.
[tex]v_f^2=v_i^2+2*a*y_f'[/tex]
[tex]y_f'=v_i/2*a =(3.63m/s)^2/2*9.8m/s^2[/tex]
[tex]y_f=0.673m[/tex]
