math question for math 1064

Question

If an object is thrown​ upward, dropped, or thrown downward and travels in a straight line subject only to​ gravity, the height h of the object above the ground​ (in feet) after t seconds is given by

h=−16t2+v0t+h0​,

where

h0

is the height of the object when

t=0

and

v0

is the velocity of the object at time

t=0.

Note that an object that is dropped​ (rather than thrown​ downward) has initial velocity

v0=0.

You are standing on a cliff that is

200

feet high. How long will it take a rock to reach the ground if

a.) you drop it

b.) you throw it downward at an initial velocity of

30

feet per​ second?

c.) How far does the rock fall in 2 seconds if you throw it downward with an initial velocity of

30

feet per​ second?

Answer 1

drop from 200 feet

h(t)= -16t^2+200=0

t^2= sqr(200/16)=10sqr2/4= 5sqr2/2=7.07/2= about 3.53 seconds

throw down with vo =30 ft/s

-16t^2-30t+200=0

8t^2+15t-100=0

t=-15/16+ (1/16)sqr(225+3200)

t=(15+sqr3425)/16

t=about 2.72 seconds

in 2 seconds

-16(4)-60+200=76

it traveled 124 feet