a ski lift is used to transport people from the base of a hill to the top. if the lift leaves the base at a…

a ski lift is used to transport people from the base of a hill to the top. if the lift leaves the base at a velocity of 15.5 m/s and arrives at the top with a final velocity of 0 m/s, what is the height of the hill? round the answer to the nearest tenth.

a ski lift is used to transport people from the base of a hill to the top. if the lift leaves the base at a velocity of 15.5 m/s and arrives at the top with a final velocity of 0 m/s, what is the height of the hill? round the answer to the nearest tenth.

Answer

Answer:

12.2

Explanation:

Step1: Identify the relevant formula

We use the kinematic - energy conservation formula $v_f^2=v_i^2 - 2gh$. Here, $v_f$ is the final velocity, $v_i$ is the initial velocity, $g = 9.8\ m/s^2$ is the acceleration due to gravity, and $h$ is the height.

Step2: Rearrange the formula for height

Rearranging $v_f^2=v_i^2 - 2gh$ for $h$ gives $h=\frac{v_i^2 - v_f^2}{2g}$.

Step3: Substitute the values

Given $v_i = 15.5\ m/s$, $v_f = 0\ m/s$, and $g = 9.8\ m/s^2$. Substitute these values into the formula: $h=\frac{15.5^2-0^2}{2\times9.8}=\frac{240.25}{19.6}\approx12.2\ m$.