Question

t My Notes Ask Your Tea As shown in the figure, a child slides down a frictionless slide o d The bottom of the silide is a height h above the ground. The child then leaves the slide horizontally H of the child in terms of h and d. (Use any veriable or symbol stated above as necessary.) striking the ground a distance d as shown. Using energy methods, determine the initial height Need Help? a

Answer 1

Let's begin with conservation of energy from H to h:

$mgH=mgh+\frac{1}{2}mv^2\rightarrow H=\left ( h+\frac{1}{2g}v^2 \right )$

From h to the floor the motion is semiparabolic so:

$d=vt\\\ h=\frac{1}{2}gt^2\rightarrow t=\sqrt{\frac{2h}{g}}\\\\ \Rightarrow d=v\sqrt{\frac{2h}{g}}\Rightarrow v=d\sqrt{\frac{g}{2h}}$

Knowing this velocity on h:

$H=\left ( \right )d=vt\\\ h=\frac{1}{2}gt^2\rightarrow t=\sqrt{\frac{2h}{g}}\\\\ \Rightarrow d=v\sqrt{\frac{2h}{g}}\Rightarrow v=d\sqrt{\frac{g}{2h}}$

Knowing this speed, we can replace it on the first equation:

$H=\left ( h+\frac{1}{2g}v^2 \right )=\left ( h+\frac{1}{2g}d^2\frac{g}{2h} \right )=\left ( h+\frac{d^2}{4h} \right )$