Explanation:
It is given that,
Mass of the dummy, m = 75 kg
Distance, d = 0.8 m
Initial speed of the dummy, u = 0
Final speed of the dummy, v = 11.2 m/s
Firstly finding the acceleration of the test car. Using third equation of motion to find it as :
[tex]v^2-u^2=2ad[/tex]
[tex]v^2=2ad[/tex]
[tex]a=\dfrac{v^2}{2d}[/tex]
[tex]a=\dfrac{(11.2)^2}{2\times 0.8}[/tex]
[tex]a=78.4\ m/s^2[/tex]
Let F is the average force. It is given by the product of mass and acceleration. It is given by :
[tex]F=ma[/tex]
[tex]F=75\times 78.4[/tex]
F = 5880 N
Taking ratios,
[tex]\dfrac{F}{W}=\dfrac{ma}{mg}[/tex]
[tex]\dfrac{F}{W}=\dfrac{a}{g}[/tex]
[tex]\dfrac{F}{W}=\dfrac{78.4}{9.8}[/tex]
[tex]\dfrac{F}{W}=8[/tex]
[tex]F=8W[/tex]
The average force acting on the dummy during the collision is 8 times of his weight. Hence, this is the required solution.
