h(t)=10+37t-t^2 when does the rocket have a height of 100 meters

Question

h(t)=10+37t-t^2 when does the rocket have a height of 100 meters

h(t)=10+37t-t^2 for how long does the rocket have a height of more that 200 meters

Answer 1

h(t) = 100 = 10+37t -t^2

t^2 -37t +90 = 0

t=37/2 + or - (1/2)sqr(37^2 - 360)= about (37+ or -31.8)/2= 5.2/2 or 68.8/2 = 2.6 or 34.4 seconds when it is at a height of 100 meters

h=200 = 10+37t-t^2

t^2-37t +190 = 0

t =37/2 + or - (1/2)sqr(37^2-760)= (37+ or - 24.7)/2 = 12.3/2 or 61.7/2 = 6.15 or 30.85 seconds at 200 meters

30.85-6.15 = 24.7 seconds above 200 meters, approximately, rounded off to one decimal place.

this doesn't seem realistic for a rocket launched on earth at sea level, as gravity would require a coefficient for the t^2 term of -4.9, not -1