Question

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. a. 4.5 m b. 7.4 m c. 3.2 m d. 1.8 m e. 2.9 m

Explanation:

Step1: Apply conservation of mechanical energy

Assume no friction, so $mgh=\frac{1}{2}mv^{2}$, where $m$ is the mass of the child, $g = 9.8\ m/s^{2}$ is the acceleration due to gravity, $h$ is the height of the slide and $v$ is the speed at the bottom.

Step2: Solve for height $h$

From $mgh=\frac{1}{2}mv^{2}$, we can cancel out the mass $m$ on both sides. Then $h=\frac{v^{2}}{2g}$.

Step3: Substitute the maximum - speed value

Given $v = 6.0\ m/s$ and $g=9.8\ m/s^{2}$, we substitute into the formula: $h=\frac{6.0^{2}}{2\times9.8}=\frac{36}{19.6}\approx1.8\ m$.

Answer:

d. 1.8 m