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. Initial mechanical energy $E_1 = mgh$ (potential energy only as initial speed $v_1 = 0$), final mechanical energy $E_2=\frac{1}{2}mv_2^{2}$ (kinetic energy only as final height $h_2 = 0$). By conservation of energy $E_1 = E_2$, so $mgh=\frac{1}{2}mv_2^{2}$.

Step2: Solve for height $h$

Cancel out the mass $m$ from both sides of the equation $mgh=\frac{1}{2}mv_2^{2}$, we get $h=\frac{v_2^{2}}{2g}$. Given $v_2 = 6.0\ m/s$ and $g = 9.8\ m/s^{2}$, then $h=\frac{6.0^{2}}{2\times9.8}=\frac{36}{19.6}\approx1.8\ m$.

Answer:

D. 1.8 m