An adventurous bungee jumper of mass 70.o kg secures on end of her cord to a bri

Question

An adventurous bungee jumper of mass 70.o kg secures on end of her cord to a bridge that is 100 m above the ground. The cord a length L= 40.0 m and behaves like an ideal spring with spring constant k= 127 N/m. After she jumps, find:

a) her speed at the point that the cord is unfurled (i.e. straight but not yet stretched).

b) the distance, x, the cord has stretched when it brings her to a stop.

c) the max acceleration experienced by the jumper.

Answers are a) 28.0 m/s b) 26.9 m c) 39.0 m/ s^2

Just don't know how to get there.

Explanation / Answer

Given thatt mass m = 70.0 kg

Length   L = 40.0 m

spring constant k = 127 N /m

a )   v = 2gh

           = 2 *9.8 * 40.0 m

          = 28.0 m/s

b ) The cord has streched to bring her stop is

           = mg( L + x ) = 1/2 k x^2

          = -kx^2 + 2mgx + 2mgL   = 0

          = -127 x^2 + 2 * 70 *9.8 x + 2 *70 *9.8 *40 =0

           = -127 x^2 + 1372 x + 54880 = 0

    solving for x we get x = 26.9 m

c ) using kinematic equation v^2 = u^2 + 2 a x

                                              ( 28.0 m/s )^2 = ( 0 ) + 2 * a * 26.9 m

                                                        a = 14.5 m/s^2

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