# 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.