A daredevil attempts to swing from the roof of a 24m high bulding to the bottom of an identical building using a 24m rope. He starts from rest with the rope horizontal, but the rope will break if the tension force in it is twice the weight of the daredevil. How high is the rope above level when it breaks? (Hint: Apply the law of conservarion of energy) Also, the building are 24m apart.

I don't understand; how can I do this without knowing the daredevil's weight?

  1. 👍 0
  2. 👎 0
  3. 👁 117
asked by Aaron
  1. please I really need help with this

    1. 👍 0
    2. 👎 0
    posted by Aaron
  2. The falling distance as a function of angle is f = 24 cos A
    where A is the angle between the line and the wall of the target building. It starts out at A = 90 and if he got there, ends at A = 0
    The component of the weight along the line is m g cos A
    (1/2) m v^2 = m g f = m g (24 cos A)
    v^2 = 48 g cos A
    The centripetal acceleration is
    v^2/r = 2 g cos A
    The tension in the line at breaking = 2 m g + m g cos A which is the mass times the centripetal acceleration
    T - m g cos A = 2 m g cos A
    T = 3 m g cos A
    so when T = 2 m g
    2 m g = 3 m g cos A
    cos A = 2/3
    A = 48.2 deg
    distance fallen = 24 cos 48.8
    = 24(2/3) = 16
    an 24 - 16 = 8 above ground
    cos A = 1
    A = 0
    That is right at the ground.

    1. 👍 0
    2. 👎 0
    posted by Damon
  3. wow, that was more elaborate than I thought it would be. Thank you so much for answering my qustion. :]

    1. 👍 0
    2. 👎 0
    posted by Aaron
  4. These were just to keep my geometry in mind.
    cos A = 1
    A = 0
    That is right at the ground.

    1. 👍 0
    2. 👎 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A 35kg child is swinging on a swing with length 2.8m to the bottom of the seat. At the highest point of the swing, the rope makes an angle of 42 degrees from vertical. Calculate the speed of the child at the bottom of the swing.

    asked by John on April 5, 2013
  2. trigonometry

    A carpenter is building a house. He is constructing the roof. The roof has an angle of elevation of 40° from the horizontal. The height he wants to make the roof is 18 feet. How far is it from the bottom edge of the roof to the

    asked by rose on October 18, 2012
  3. Math C30 ( trig )

    A roof in the shape of an upside down cosine wave is to be buile to cover an arena. The arena is 24m wide, the height of the roof at either side wall is 5m, and the maximum height of the roof is 9m. A) write a function that gives

    asked by Don on November 6, 2011
  4. Physics

    A daredevil decides to jump across a 15 m wide canyon on his motorcycle. The opposite side of the canyon is 3 m lower than the side the daredevil starts on. The daredevil drives his motorcycle off the cliff at a speed of 27 m/s.

    asked by Olivia on October 17, 2013
  5. Physics

    A gymnist is swinging on a high bar. The distance between his waist and the bar is 1.1M. At the top of the swing his speed is momentarily zero. ignoring friction and treating the gymnist as if all his mass is located at his waist,

    asked by Cavin on February 27, 2007
  6. Physics Prob.

    A 22.0 kg child plays on a swing having support ropes that are 2.00 m long. A friend pulls her back until the ropes are 45.0 ∘ from the vertical and releases her from rest. What is the potential energy for the child just as she

    asked by Justin on November 24, 2017
  7. Physics

    A ball thrown horizontally at 21m/s from the roof of a building lands 24m from the base of the building. Now high is the building?

    asked by Arman on September 13, 2016
  8. PHysics

    .) Bailey has taken up parkour. She attempts to clear the gap between two buildings. Bailey is on a roof which is 50m high and she is attempting the jump to a building that is 42m high. a.) If the two buildings were built touching

    asked by Heidi on November 12, 2010
  9. physics

    A child swinging on a swing set hears the sound of a whistle that is being blown directly in front of her. At the bottom of her swing when she is moving toward the whistle, she hears the higher pitch, and at the bottom of her

    asked by Trace on March 3, 2011
  10. college physics

    A pendulum is 0.9 m long and the bob has a mass of 1.0 kg. At the bottom of its swing, the bob's speed is 1.6 m/s. What is the tension in the string at the bottom of the swing

    asked by kayla on February 11, 2010

More Similar Questions