Question

test information
description: show all you work, including units, on separate paper. follow the \problem solving method\. this final exam is cumulative and covers material from the entire course.
instructions: from the list of choices, select the one best answer.
multiple attempts: not allowed. this test can only be taken once.
force completion: this test can be saved and resumed later. your answers are saved automatically.
question completion status: question numbers 1 - 62 with some marked as completed
question 35
1.6 points
a 22 kg child starts from rest at the top 5.0 m frictionless slide. what is the speed of the child when she reaches the bottom?
options: 9.9 m/s, 14 m/s, 11 m/s, 6.7 m/s

Explanation:

Step1: Identify the principle

Use conservation of mechanical energy (since the slide is frictionless, mechanical energy is conserved). The initial energy is gravitational potential energy (\(U = mgh\)) and initial kinetic energy (\(K_i = 0\) as it starts from rest). At the bottom, potential energy is \(U_f = 0\) (taking bottom as reference) and kinetic energy is \(K_f=\frac{1}{2}mv^2\). So, \(mgh=\frac{1}{2}mv^2\).

Step2: Simplify the equation

Cancel mass \(m\) from both sides: \(gh=\frac{1}{2}v^2\).

Step3: Solve for \(v\)

Rearrange to \(v = \sqrt{2gh}\). Substitute \(g = 9.8\ m/s^2\) and \(h = 5.0\ m\):
\(v=\sqrt{2\times9.8\times5.0}=\sqrt{98}\approx9.9\ m/s\).

Answer:

9.9 m/s