Answer to Question #245901 in Physics for Kapalu

Question

1. An archer shoots an arrow from a bow. Assuming the force exerted by the bow on the arrow is a spring force,

in one dimension

(a) write an expression of the force exerted on the arrow.

(b) solve the equation in (a) and determine the velocity with which the arrow leaves the bow.

(c) In three dimension write the expression of the force exerted by the bow on the arrow.

Answer 1

(a) The force is

$$F=kx.$$

(b)

$$ma=kx, \\\space\\ m\frac{v^2}{2x}=kx,\\\space\\ v=x\sqrt{\frac{2k}{m}}.$$

(c) The force is

$$\vec F=k_1x_1\hat i+k_2x_2\hat j+k_3x_3\hat k.$$