Answer:
k = 52.2 N / m
Explanation:
For this exercise we are going to use the conservation of mechanical energy.
Starting point. When it is 30 m high
Em₀ = K + U = ½ m v² + m g h
Final point. Right when you hit the water
= K_{e} = ½ k x²
in this case the distance the bungee is stretched is 30 m
x = h
as they indicate that there are no losses, energy is conserved
Em₀ = Em_{f}
½ m v² + m g h = ½ k h²
k =
let's calculate
k =
k = 52.2 N / m
Answer:
Final Speed of Dwayne 'The Rock' Johnson = 15.812 m/s
Explanation:
Let's start out with finding the force acting downwards because of the mass of 'The Rock':
Dwayne 'The Rock' Johnson: 118kg x 9.81m/s = 1157.58 N
Now the problem also states that the kinetic friction of the desk in this problem is 370 N
Since the pulley is smooth, the weight of Dwayne Johnson being transferred fully, and pulls the desk with a force of 1157.58 N. The frictional force of the desk is resisting this motion by a force of 370 N. Subtracting both forces we get the resultant force on the desk to be: 1157.58 - 370 = 787.58 N
Now lets use F = ma to calculate for the acceleration of the desk:
787.58 = 63 x acceleration
acceleration = 12.501 m/s
Finally, we can use the motion equation:
here u = 0 m/s (since initial speed of the desk is 0)
a = 12.501 m/s
and s = 10 m
Solving this we get:
Since the desk and Mr. Dwayne Johnson are connected by a taught rope, they are travelling at the same speed. Thus, Dwayne also travels at 15.812 m/s when the desk reaches the window.