Question

The eagle flies at a speed of 9 m / s, while holding its prey in its claws. At one point, its prey is torn from its claws and begins to fall from a height of 12.5 m. Find the intensity of the speed at which the prey hits the ground. When considering ignore the influence of air resistance.

Answer 1

The prey will have the horizontal velocity $v_x=9\ \dfrac{m}{s}$. Let's find its vertical velocity. Let's first find the time that the pray takes to reach the ground:

$$h=\dfrac{1}{2}gt^2,$$ $$t=\sqrt{\dfrac{2h}{g}}=\sqrt{\dfrac{2\cdot12.5\ m}{9.8\ \dfrac{m}{s^2}}}=1.6\ s.$$

Then, we can find the vertical velocity of the pray:

$$v_y=v_0-gt=0-9.8\ \dfrac{m}{s^2}\cdot1.6\ s=-15.68\ \dfrac{m}{s}.$$

Finally, we can find the speed at which the pray hits the ground from the Pythagorean theorem:

$$v=\sqrt{v_x^2+v_y^2},$$ $$v=\sqrt{(9\ \dfrac{m}{s})^2+(-15.68\ \dfrac{m}{s})^2}=18.1\ \dfrac{m}{s}.$$