Any object that is falling or vertically projected into air had its height above the ground h (t), in feet....

Question

after T seconds in motion, modeled by the quadratic funtion h(t)=-16t^2+Vot+Ho, where V initial is the original velocity of the object, in ft per sec, and h initial is the original height in feet above the ground. Height of a rock a projected. A rock is projected upward from ground level with an inital velocity of 90ft per sec. Let t represent the amount of time elapsed after it is thrown. A. Give function h that it describes the height of the rock as a function of t. B. If the heighth of the rock is at 30ft what is the time? C.If the height of the rock is at 60ft, what's the time? D. If the height of the rock is at 120ft whats the time?E.How high will the rock be 1.5sec after thrown? F.What is the max height attained by the rock? After how many secs?G. After how many sec will it hit the ground? PLEASE PLEASE HELP ME HERE IM STUCK AND MY CURRENT ANSWERS ARE ALL WRONG!

Answer 1

the first equation
h(t)=-16t^2+Vot+Ho
will be used to answer A
Ho=0, Vo=90
h(t)=90*t-16*t^2

and B
30=90*t-16*t^2
this is a quadratic. select the positive root
0=-30+90*t-16*t^2

and C
0=-60+90*t-16*t^2
again, thake the positive root

D.
0=-120+90*t-16*t^2

for E
h(1.5)=90*1.5+16*1.5^2

F is a bit trickier. At apogee (max height) the velocity is zero.
The velocity follows the equation
v(t)=V0-32*t
set equal to zero and plug in Vo=90
t=90/32

For G
h(t)=0 happens at time equal zero and at time
0=90*t-16*t^2
see how t=0 is the first h(t)=0?
t=90/16 is when it returns to the ground

j

Answer 2

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