Hey there! Sign in to join this conversationNew here? Join for free to post


Announcements Posted on
Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
    • Thread Starter

    a bungee jumper leaps off the starting platform at time t=0 and rebounds once during the first five seconds. with velocity measured downward, for t in seconds and 0<t<5, the jumpers velocity is approximated by v(t)= -4t^2 +16t meters/second.
    a. how many meters does the jumper travel in the first five seconds?
    b. where is the jumper relative to the starting point at the end of five seconds?
    c. what does 0-5 v(t) dt represent in terms of the jump?

    a) v = ds/dt, so s = integral of v dt = 8t^2 - (4/3)t^3 (+c)

    However, distance travelled is scalar unlike displacement which is a vector. Therefore, we must take into account which intervals of t give negative v, so we must solve v < 0

    v = 16t - 4t^2 = 4t(4-t) = 0 when t = 0 or 4. When t = 2, v = 16 > 0, therefore v < 0 when t < 0 or t > 4. For the interval 0 < t < 5 that we are interested in, this means v is negative for 4 < t < 5

    Therefore, distance travelled = (integral btwn 4 and 0 of v dt) - (integral btwn 5 and 4 of v dt) = 128/3 + 28/3 = 156/3 = 52 m

    b) The jumpers position is determined by displacement, so s = integral btwn 5 and 0 of v dt = 100/3

    Therefore, the jumper is 100/3 m below the starting position.

    c) This represents displacement in the downwards direction, relative to the starting position.
Write a reply…


Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: April 26, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Which is your favourite handheld games console?
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.