Answer to Question #113445 in Physics for SRUUL

Question

An arrow weighing 7 g is mounted on a square piece of wood weighing 1 kg
penetrated to a depth of 8 cm. Then place the square stick with the arrow on a non-abrasive horizontal surface
How many centimeters deep will the arrow penetrate when it is placed and fired again?

Answer 1

$$\Delta E\backsim l$$

$$\Delta E_1=0.5v^2\frac{mM}{m+M}, \Delta E_2=0.5mv^2$$

$$l_2=l_1\frac{m+M}{M}=8\frac{0.007+1}{1}=8.056\ cm$$