Please help! I'm having the worst time figuring this out.

Question

3. One of the fireworks is launched from the top of the building that is 70ft tall with an initial
upward velocity of 150 ft/sec.
a. What is the equation for this situation?
b. When will the firework land if it does not explode? I think the firework will land in 3 seconds.

Answer 1

Well, who does feet any more but anyway in that system
g = -32 ft/s^2

v = Vi - g t
v = 150 - 32 t
at the top, v = 0 so
0 = 150 - 32 t
t = 4.69 seconds to the top

h = Hi + Vi t - (1/2)gt^2
h = Hi + Vi t - 16 t^2
h = 70 + 150 t - 16 t^2
so at the top
h = 70 + 150(4.69) -16 (4.69)^2
h = 421.5 feet high at the top

Now it has to fall from there
how long to fall from 421.5 ft
421.5 = (1/2)(32)t^2
t to fall = 5.13 seconds fall time
so total time in air =4.69+5.13
= 9.82 seconds

note I could have solved for total t directly by saying
0 = 70 + 150 t - 16 t^2
but I did not want to solve the quadratic equation so did upward and downward as separate problems.

Answer 2

Thank you! Do you know how I can make a table that shows the height from time t=0 until it hits the ground?

Answer 3

here is the height versus time t

h = 70 + 150 t - 16 t^2