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help me with this vertical motion problem please?
Fireworks are shot upwards at an initial velocity of 125 ft per sec from a platform 3 ft above the ground . find out how long it will take the rocket to hit the ground.
use the formula h= -16t^2 + vt + s
(h= feet, t=time in seconds, v=velocity, s= initial height)
all i know is that h should be zero, and s should be 3, and v should be 125. but then i dont know how to solve it. please tell me the right answer and explain how you did it :)
10 points :)
1 Answer
- Anonymous1 decade agoFavorite Answer
h = -16t^2 + vt + s
0 = - 16t^2 + 125t + 3
Multiply by - 1:
16t^2 - 125t - 3 = 0
Solve using the quadratic formula.
The roots of ax^2 + bx + c = 0 are:
x = [ - b +/- sqrt(b^2 - 4ac) ] / (2a)
For this question t replaces x, and the roots are:
t = [ 125 +/- sqrt(125^2 + 4 * 16 * 3) ] / (2 * 16)
= [ 125 +/- sqrt(15817) ] / 32
= [ 125 +/- 125.766 ] / 32
The positive value of t is:
t = [ 125 + 125.766 ] / 32
= 7.84 sec to 3 sig. fig.