Respuesta :
Answer:
The velocity of the toboggan is 7.51 m/s.
Explanation:
Given that,
Mass of toboggan = 10 kg
Mass of girl =40 kg
Mass of boy = 45 kg
Velocity = 2 m/s
Suppose that h = 3.2 m
We need to calculate the velocity
Using conservation of energy
[tex]K.E_{1}+P.E_{1}=K.E_{2}+P.E_{2}[/tex]
[tex]\dfrac{1}{2}(m_{t}+m_{g}+m_{b})v^2+(m_{t}+m_{g}+m_{b})gh=\dfrac{1}{2}(m_{t}+m_{g}+m_{b})v^2+0[/tex]
Put the value into the formula
[tex]0+(10+40+45)\times9.8\times3.2=\dfrac{1}{2}(10+45+40)v^2[/tex]
[tex]v^2=\dfrac{95\times9.8\times3.2\times2}{95}[/tex]
[tex]v=\sqrt{62.72}\ m/s[/tex]
[tex]v=7.91\ m/s[/tex]
The velocity of boy is
[tex]v_{b/t}=v_{t}-v_{b}[/tex]
[tex]v_{b}=v_{t}-2[/tex]
We need to calculate the velocity of the toboggan
Using principle of momentum
[tex](m_{t}+m_{g}+m_{b})v=(m_{t}+m_{g})v_{t}+m_{b}v_{b}[/tex]
Put the value into the formula
[tex](10+40+45)\times7.91=(10+45)\times v_{t}+45\times(v_{t}-2)[/tex]
[tex]751.45=55v_{t}+45v_{t}-90[/tex]
[tex]751.45+90=130v_{t}[/tex]
[tex]v_{t}=\dfrac{751.45}{100}[/tex]
[tex]v_{t}=7.51\ m/s[/tex]
Hence, The velocity of the toboggan is 7.51 m/s.
