Answer:
8.04924 m/s²
Explanation:
r = Distance the child is from the center = 4.65 m
[tex]\alpha[/tex] = Angular acceleration = 0.745 rad/s²
[tex]\omega[/tex] = Angular velocity = 1.25 rad/s
Velocity is given by
[tex]v=r\omega\\\Rightarrow v=4.65\times 1.25\\\Rightarrow v=5.8125\ m/s[/tex]
Radial acceleration is given by
[tex]a_r=\frac{v^2}{r}\\\Rightarrow a_r=\frac{5.8125^2}{4.65}\\\Rightarrow a_r=7.265625\ m/s^2[/tex]
Tangential acceleration is given by
[tex]a_t=\alpha r\\\Rightarrow a_t=0.745\times 4.65\\\Rightarrow a_t=3.46425\ m/s^2[/tex]
The resultant acceleration is given by
[tex]a=\sqrt{a_r^2+a_t^2}\\\Rightarrow a=\sqrt{7.265625^2+3.46425^2}\\\Rightarrow a=8.04924\ m/s^2[/tex]
The magnitude of the acceleration of the child is 8.04924 m/s²
