Question

The arrow is shot with the bow vertically upwards. The spring gives the arrow a speed of 19 m / s. How high does the arrow rise?

Answer 1

Let's first find the time that the arrow takes to reach the maximum height from the kinematic equation:

$$v=v_0-gt,$$ $$0=v_0-gt,$$ $$t=\dfrac{v_0}{g}=\dfrac{19\ \dfrac{m}{s}}{9.8\ \dfrac{m}{s^2}}=1.94\ s.$$

Finally, we can find the maximum height that the arrow can reach from the kinematic equation:

$$y=v_0t-\dfrac{1}{2}gt^2,$$ $$y=19\ \dfrac{m}{s}\cdot1.94\ s-\dfrac{1}{2}\cdot9.8\ \dfrac{m}{s^2}\cdot(1.94\ s)^2=18.42\ m.$$

Answer:

$y=18.42\ m.$