A train is traveling at a constant speed of 88 ft/sec when Casey the engineer no

Question

A train is traveling at a constant speed of 88 ft/sec when Casey the engineer notices some hooligans preparing to drop a refrigerator from the top of the bridge across the tracks in front of the train. Casey jams on the brakes and applies a constant deceleration of 25ft/sec/sec. Sad to say, this isn't good enough. The speedometer reads 13ft/sec as it is smashed to bits by the falling fridge. Assume that the speedometer was 9ft above the track and the fridge was dropped from 25ft above the track.

Q1. How many seconds after the brakes were applied did the hooligans drop the fridge?

Q2. How far from the fridge did Casey see the hooligans' plan, if his reaction time was 0.5 seconds?

Explanation / Answer

time taken by the train to decelerate from 88ft/sec to 13ft/sec with deceleration of 25ft/sec/sec is t=(13-88)/-25 =3sec

for the fridge, initial height = 25ft , final height = 9ft , distance travelled s=25-9=16ft ,initial velocity u=0 , acceleration a=32ft/sec/sec

s=ut+(1/2)at2

=>16=0t +(1/2)*32t2

=>16=0t +16t2

=>16t2=16

=> t =1

fridge takes 1 sec to fall from 25ft to 9ft

Q1)

time between application of brakes and frigde drop = 3 -1 =2 sec

Q2)

casey reaction time was 0.5 seconds

time since Casey see the hooligans' plan before reaching fridge=0.5+3 =3.5seconds

distance travelled during his reaction time =0.5*88 =44ft

v=13,u=88,a=-25 ,s=[v2-u2]/2s

distance travelled after applying breakes =[132-882]/(2*-25)

distance travelled after applying breakes =151.5 ft

distance from the fridge that Casey see the hooligans' plan =44+151.5 =195.5 ft

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