Answer:
a).[tex]I=981J[/tex]
b).[tex]V_f=3.756m/s[/tex]
c).[tex]v_1=3.04m/s[/tex]
d).[tex]y'=0.47m[/tex]
Explanation:
Given:
[tex]m=67kg[/tex],[tex]h_i=0.720m[/tex],[tex]t_1=0s[/tex],[tex]t_2=0.8s[/tex]
a).
[tex]F=9200t-11500t^2[/tex]
[tex]I=\int\limits^a_b {F} \, dx =\int\limits^.8_0 {9200t-11500t^2} \, dt[/tex]
[tex]I=4600t^2-3833.33t^3|0,0.8[/tex]
[tex]I=981J[/tex]
b).
[tex]v_f^2=v_i^2+2*a*y[/tex]
She began in rest so vi=0
[tex]v_f=\sqrt{2*g*y}=\sqrt{2*9.8m/s^2*0.720m}=\sqrt{14.112 m^2/s^2}[/tex]
[tex]V_f=3.756m/s[/tex]
c).
Impulse total=momentum total
[tex]I_i-I_f=m_1*v_1-m_1*v_f[/tex]
[tex]981-(67kg*9.8m/s^2*0.8)=67kg*v_1-67*kg*(-3.756m/s)[/tex]
Solve to v1
[tex]v_1=\frac{204.068kg*m/s}{67kg}[/tex]
[tex]v_1=3.04m/s[/tex]
d).
[tex]v_f^2=v_i^2+2*a*y'[/tex]
[tex]v_f=0[/tex]
[tex]y=\frac{-v_i^2}{2*g}=\frac{-(3.04m/s)^2}{2*-9.8m/s^2}[/tex]
[tex]y'=0.47m[/tex]
