math homework help

Question

A rider on mountain one jumps off a ledge. Her path is modelled by the relation h = -0.3d^2 + 1.2d + 1.5, where h is her height above the ground and d is her horizontal distance from the ledge both in meters
from what height did the rider jump
find the zeros
what is her horizontal distance when she hits the ground
what is her max height above ground
what is her horizontal distance when she reaches her max height

Answer 1

initial height was 1.5 when d= 0

h(d)=-.3d^2 +1.2d + 1.5

h(0) = 1.5

0 = -3d^2 +12d +15

d^2 -4d - 5 = 0

(d-5)(d+1) = 0, zeros are 5 and -1

d = 5 when it hits the ground (ignore the negative d)

max h is when h'=0

h'= -.6d +1.2 = 0

d = 12/6= 2

max h = -.3(4) + 1.2(2) + 1.5

= -1.2 + 2.4 + 1.5

= 2.7 = maximum height when horizontal distance = 2