Question

test information
description
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:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
moving to another question will save this response. question 7 of 20
question 7 5 points save answer
an engineer is asked to design a playground slide such that the speed a child reaches at the bottom does not exceed 6.0 m/s. determine the maximum height that the slide can be. friction is negligible.
2.9 m
3.2 m
7.4 m
1.8 m
4.5 m

Explanation:

Step1: Apply conservation of mechanical energy

Since friction is negligible, the potential energy at the top \(mgh\) is converted to kinetic energy at the bottom \(\frac{1}{2}mv^{2}\). So, \(mgh=\frac{1}{2}mv^{2}\).

Step2: Solve for height \(h\)

Cancel out the mass \(m\) from both sides of the equation \(mgh=\frac{1}{2}mv^{2}\). We get \(h = \frac{v^{2}}{2g}\). Given \(v = 6.0\ m/s\) and \(g=9.8\ m/s^{2}\), then \(h=\frac{6.0^{2}}{2\times9.8}=\frac{36}{19.6}\approx1.8\ m\)

Answer:

1.8 m