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

Answer 1

Answer:

1.8 m

Step-by-step explanation:

The motion from the top of the slide is virtually under gravity. The motion starts from rest. We use the equation of motion

$v_f^2 = v_i^2 + 2as$

$v_f$ and $v_i$ are the final and initial velocities, respectively, a is the acceleration and s is the displacement.

For this motion, initial velocity is 0 m/s, final velocity is 6 m/s, a is the acceleration of gravity (9.8 m/s2) and s is the height, h.

$v_f^2 = v_i^2 + 2gh$

$6^2 = 0^2 + 2\times9.8h$

$h=\dfrac{36}{19.6}=1.8 \text{ m}$