Consider again the situation in number 2 for the following: Van Helsing shoots a 150g stake from a crossbow. Find the stake’s speed if we treat the crossbow as a spring with k = 600N/m that is drawn back 22cm. a. If the stake takes 0.06s to launch, what is the average force from the crossbow on the bolt? b. If he releases the 2kg crossbow when it fires, what is the recoil speed of the crossbow? c. If the stake rises to a height of 4m, what is its velocity at the peak of its trajectory?

According to the law of conservation of energy , the total energy in a system will be conserved .So while using spring to shoot , the initial energy will be the potential energy of the  spring , which is , $E_s=\frac{1}{2}k{A}^2$ and this entire energy will be used as kinetic energy of the stake , which is , $E_k=\frac{1}{2}m{v}^2$ , where $k=600 N/m$ is the spring constant, $\begin{array}{rcl}A& =& 22 cm\\ & =& 0.22 m\end{array}$ is the amplitude of the spring , $m$ is the mass of the stake and $v$ is the velocity of the stake.

According to the law of kinematics , the displacement is $s=ut+\frac{1}{2}a{t}^2$ , where u is the initial velocity , t is the time taken and a is the acceleration. Force acting on an object is defined as the product of mass$\left(m\right)$ and acceleration $\left(a\right)$ of the object, that  is , $F=ma$

When the stake is released , as it moves to the height it's kinetic energy , which is , $E_k=\frac{1}{2}m{v}^2$ will reduce and it will converted to potential energy and at maximum height the kinetic energy will be equal to potential energy, which is ,$E_p=mgh$. , where $g=9.8 m/s^2$ is the acceleration due to gravity and $h$ is the height .

According to the law of conservation of momentum , in an isolated system , the initial momentum will be equal to the final momentum, where momentum is the product of mass and velocity , that is ,$p=mv$.