Question

An engineer is asked to design a playground slide such that the speed a child reaches
at the bottom does not exceed 4.0 m/s. Determine the maximum height that the slide
can be.?Given, g = 9.8 m/s2​

Answer 1

An engineer is asked to design a playground slide such that the speed a child reaches at the bottom does not exceed 4.0 m/s.

We have to determine the maximum height that the slide can be...

solution :

as external force acting on a child during sliding on the slide be zero, mechanical energy at the top of slide will be equal to the mechanical energy at the bottom.

at the top,

mechanical energy = potential energy = mgh

at the bottom,

mechanical energy = kinetic energy = 1/2 mv²

∵ mechanical energy at the top = mechanical energy at the bottom

∴ mgh = 1/2mv²

⇒h = v²/2g

here, v = 4 m/s , g = 9.8 m/s²

so, h = (4)²/(2 × 9.8) = 0.816 m

Therefore the maximum height that slide can be, is 0.816 m.

Answer 2

Answer:

Entire PE is converted to KE when the child reaches bottom

So

KE = PE

12mv2=mgH12mv2=mgH

or H=v22g=162×9.8=.816mH=v22g=162×9.8=.816m