A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2.
-What is the speed of the rock as it hits the ground?
A)11.5 m/s
B)26.8 m/s
C)24.5 m/s
D)16.2 m/s

Question

Quizplus · Accepted Answer

The speed of the rock as it hits the ground can be found using the conservation of energy principle. The initial kinetic energy plus the initial potential energy will equal the final kinetic energy (since we're assuming no air resistance). The initial potential energy can be calculated using $PE = mgh$, where $h$ is the height of the building. The initial kinetic energy is given by $KE = \frac{1}{2}mv^2$, where $v$ is the initial speed of the rock. The final kinetic energy will have the same form, but we'll solve for the final speed. Since mass $m$ is constant and does not need to be known to solve the problem, we can set the sum of the initial kinetic and potential energies equal to the final kinetic energy and solve for the final speed. The calculation involves finding the initial kinetic and potential energies, setting their sum equal to the final kinetic energy, and solving for the final speed. The exact speed can be calculated using the formula derived from the conservation of energy, taking into account the height from which the stone is thrown and its initial speed. The correct answer, after performing the calculations with the given values (initial speed, height of the building, and acceleration due to gravity), is 26.8 m/s.

A Stone Is Thrown with an Initial Speed of 11