# Question #b2ebb

Feb 6, 2017

I got $2.6 m$

#### Explanation:

I would say that the Elastic Potential Energy of the spring is converted into Kinetic Energy for the brick and so we have:
$\frac{1}{2} k {x}^{2} = \frac{1}{2} m {v}^{2}$
rearranging:
$v = x \sqrt{\frac{k}{m}} = 0.25 \sqrt{\frac{1250}{1.5}} = 7.2 \frac{m}{s}$ which should be the velocity with which the brick leaves the spring.
Using Kinematics we have that:
${v}_{f}^{2} = {v}_{i}^{2} = 2 a h$
where:
${v}_{f} = 0$ at the top of the trajectory;
${v}_{i} = 7.2 \frac{m}{s}$
$g = - 9.8 \frac{m}{s} ^ 2$ is the downwards acceleration of gravity;
$h$ is the eight reached.
So we get:
$0 = {\left(7.2\right)}^{2} - 2 \cdot 9.8 h$
rearranging:
$h = {\left(7.2\right)}^{2} / \left(2 \cdot 9.8\right) = 2.6 m$