Question #b48bd
1 Answer
Jun 17, 2017
The expression for diver's height above the water line is given as a function of time
#h(t)=at^2+bt+10# ......(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. - 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) - She reaches back at the platform height in
#1s#
Equation (1) becomes
#10=a+b+10#
#=>a=-b# ........(3) - 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.