Question 210708
You need to find at what time, t, will the height, h, is equal to 35 metres.
Set h = 35 and solve for t.
{{{35 = -4.9t^2+30t+1.6}}} Subtract 3 from both sides.
{{{-4.9t^2+30t+33.4 = 0}}} Solve this quadratic equation using the quadratic formula:{{{t = -b+-sqrt(b^2-4ac))/2a}}} In this equation, a = -4.9, b = 30, and c = -33.4.  Make the appropriate substitutions into the formula:
{{{t = (-30+-sqrt(30^2-4(-4.9)(33.4)))/2(-4.9)}}} Evaluate:
{{{t = (-30+-sqrt(900-(-654.64)))/(-9.8)}}}
{{{t = (-30+-sqrt(1554.64))/(-9.8)}}}
{{{t = (-30+-39.43)/(-9.8)}}}
{{{t = (-30+39.43)/(-9.8)}}} or {{{t = (-30-39.43)/(-9.8)}}}
{{{t = -0.962}}} or {{{highlight(t = 7.08)}}} Discard the negative solution
It will take 7.08 seconds for the ball to reach a height of 35 metres.