Children slide down a frictionless water slide that ends at a height of 1.80 m above the pool. if a child starts from rest at point a and lands in the water at point b, a horizontal distance l = 2.42 m from the base of the slide, determine the height h of the water slide.

0.813 m

Explanation:

Given

height at which slide ends is h=1.8 m

Horizontal distance L=2.42 m moved by child from slide base to pool

At slide end Child has only horizontal velocity

horizontal velocity is given by

where H=height of slide

time taken by child to complete 1.8 m height

Horizontal distance moved in this time

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft