Answer:
a)11,71 m/s
b)12.73 m/s
Explanation:
We apply the conservation principle because there is no friction between the hill and the sled:
Total initial energy (Ei) = Total initial energy (Ef), Equation(1)
We define:
K = Kinetic energy = [tex]\frac{1}{2}*m*v^{2}[/tex]
U = Potential energy = [tex]m*g*h[/tex]
m = mass (kg)
v = velocity (m/s)
h = height (m)
g = gravity acceleration = [tex]9.8m/s^{2}[/tex]
A) hi=7m, hf=0 ,vi=0 , vf=?
[tex]Ei=Ef\\Ki+Ui=Kf+Uf[/tex]
[tex]1/2*m*vi^{2} +m*g*hi= 1/2*m*vf^{2} +m*g*hf[/tex]
[tex]0+m*g*hi=1/2*m*vf^{2}+0[/tex]
[tex](2*m*g*hi)/m=vf^{2}[/tex]
[tex]vf=\sqrt{2*g*hi}[/tex]
[tex]vf=\sqrt{2*9.8*7}[/tex]
[tex]vf=11.71 m/s[/tex]
Answer: She reaches the base of the hill with speed of 11.22 m/s
B) hi=7 m, vi=5 m/s, hf=0, vf=?
[tex]m*g*hi+1/2*m*vi^{2} =m*g*hf+1/2*m*vf^{2} [/tex]
We divide all terms by m
[tex]g*hi+1/2vi^{2} =g*hf+1/2*vf^{2}[/tex]
[tex]9.8*7+1/2*5^{2} =1/2*vf^{2}[/tex]
[tex]2(68.6+12.5)=vf^{2}[/tex]
[tex]162.2=vf^{2}[/tex]
[tex]vf=\sqrt{162.2}[/tex]
[tex]vf=12.73 m/s[/tex]
Answer: She will move with a speed of 12.73 m/s when she reaches the base of the hill
