Critical Thinking Assessment. Two children of equal mass, Joe and Linda, slide d

Question

Critical Thinking Assessment. Two children of equal mass, Joe and Linda, slide down two frictionless home-made water slides and then, after landing on the ground at the bottom of the slide, skid a distance d across the wet grass until being slowed to a stop by friction. Linda's slide is twice as high as Joe's. How many times farther does Linda skid across the grass? Carefully explain your answer in terms of conservation of energy and ratio reasoning, and draw a box around your final answer! A complete essay is not required for this problem.

Explanation / Answer

here,

the height of Linda , hl = 2 * height of Joe(hj)

for Linda

let the speed gained at the bottom of slide be vl

using conservation of energy

m * g * hl = 0.5 * m * vl^2

vl = sqrt(2 * g * hl)

for Joe

the speed gained at the bottom of slide be vj

using conservation of energy

m * g * hj = 0.5 * m * vj^2

vj = sqrt(2 * g * hj)

accelration due to friction is same for both say a

let the distance travelled before stopping be dl and dj

for Linda

vl^2 - u^2 = 2 * a * dl

2 * g * hl = 2 * a * dl

dl = g * hl/a

for Linda

vj^2 - u^2 = 2 * a * dj

2 * g * hj = 2 * a * dj

dj = g * hj/a

dl/dj = ( g * hl/a) /( g * hj/a)

dl/dj = hl/ha = 2

dl = 2 * dj

so, the distance travelled by Linda is 2 times the distance travelled by Joe on grass

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