Question #b48bd

1 Answer
Jun 17, 2017

The expression for diver's height above the water line is given as a function of time #t#

#h(t)=at^2+bt+10# ......(1)

  1. At #t=0#, the function reduces to
    #h(0)=10#
    Implies that diving platform is located at a height of #10m# above the water line.
  2. She reaches maximum height of #0.75m# above the platform in #0.5s#. Equation (1) becomes

    #h(t)=10+0.75=a(0.5)^2+b(0.5)+10#
    #=>0.75=0.25a+0.5b#
    Multiplying both sides with #4# we get
    #a+2b=3# .......(2)

  3. She reaches back at the platform height in #1s#
    Equation (1) becomes
    #10=a+b+10#
    #=>a=-b# ........(3)
  4. Using (3), equation (2) becomes
    #-b+2b=3#
    #b=3#
    and #:.a=-3#

Equation (1) becomes

#h(t)=-3t^2+3t+10#

Comparing with general kinematic expression

#h(t)=1/2at^2+ut+10#
we see that initial velocity of the diver #b=3ms^-1#
and acceleration #2a=-6ms^-2#.
#-ve# sign shows that acceleration is acting in a direction opposite to direction of initial velocity.