A shot putter can throw the shot with an initial velocity of 20 m/s from a height of 1.8 m at an angle of 30 degrees to the horizontal. With what speed does the shot hit the ground?
A)10 m/s
B)11.63 m/s
C)20 m/s
D)20.86 m/s

Question

Quizplus · Accepted Answer

The speed at which the shot hits the ground can be found using the principle of conservation of energy or by resolving the motion into horizontal and vertical components and then using kinematic equations. The initial kinetic energy is converted into kinetic and potential energy at the point of impact. The initial velocity components are $V_x = V \cos(\theta)$ and $V_y = V \sin(\theta)$, where $V = 20$ m/s and $\theta = 30^\circ$. The final speed can be found using the equation $V_{final} = \sqrt{V_x^2 + (V_y - gt)^2}$, where $g$ is the acceleration due to gravity and $t$ is the time of flight. However, a simpler and more direct approach involves recognizing that the horizontal component of velocity remains constant throughout the flight, and the vertical component changes due to gravity. The final speed is a combination of these components, which can be calculated without explicitly finding the time of flight. The correct answer, taking into account both the initial kinetic energy and the potential energy at the height of 1.8 meters, leads to a final speed of approximately 20.86 m/s, considering the conservation of energy in both the horizontal and vertical directions.

A Shot Putter Can Throw the Shot with an Initial