Acceleration, speed, and final velocity. (Please answer all questions and show s

Question

Acceleration, speed, and final velocity. (Please answer all questions and show steps)

A convict of mass 100 kg wants to escape out the window of his cell. So he ties together some old bed sheets to form a rope that he unrolls out the window. Unfortunately, the sheets can only support a tension of 800 N without tearing. The convict figures, however, that if he slides down the sheets with the right constant acceleration, he can avoid tearing the sheets. What is the acceleration that would avoid tearing the sheets? If his 4th-story window is 16 m above the ground, how fast will he be moving when he hits the ground? For comparison, from what height could he jump without using the sheets (that is, with the usual acceleration of 10 m/s2) that would give him this same final velocity as he hits the ground?

Explanation / Answer

here,

mass of the convict , m = 100 kg

tension in the string , t = 800 N

(a)

let the accelration be a

m*g - t = m*a

100 *9.8 - 800 = 100 * a

a = 1.8 m/s^2

the accelration is 1.8 m/s^2

(b)

height of the window , h = 16 m

let the speed when hits the ground be v

v^2 - u^2 = 2 * a * h

v^2 - 0 = 2 * 1.8* 16

v = 7.59 m/s

the speed of the convict is 17.71 m/s when he hits the ground

(c)

let the height be h

using third equation of motion

v^2 - u^2 = 2 * g * h

7.59^2 - 0 = 2 * 9.8 *h

h = 2.94 m

the height could he jump from is 2.94 m

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