Question 1032514
The values for the heights are given recursively as 

{{{a[n+1] = a[n] + d[n]}}}, where {{{d[n]}}} is an AP with {{{a[1] = -5}}} and common difference d = -10. Indeed, 

{{{d[n] = -5 + (n-1)(-10) = 5 - 10n}}}.  Now
{{{a[2] = a[1] + d[1]}}}, 
{{{a[3] = a[2] + d[2]}}}, 
{{{a[4] = a[3] + d[3]}}},

.........................

{{{a[n-1] = a[n-2] + d[n-2]}}}, 
{{{a[n] = a[n-1] + d[n-1]}}},
{{{a[n+1] = a[n] + d[n]}}}, 

Adding all the corresponding sides of these equations gives

{{{a[n+1] = a[1] +d[1] + d[2]}}}+...+ {{{d[n]}}}.
<==> {{{a[n+1] = a[1]+ (n/2)(-5 + 5-10n) = 1000 - 5n^2}}}, for {{{n>=0}}}.

==> {{{a[n] = 1000 - 5(n-1)^2}}}.

Hence let {{{a[n] = 1000 - 5(n-1)^2 = 0}}}.

==> {{{n = 1+ 10sqrt(2) = 15.14}}} seconds, the time her purse reaches the ground.