In order to determine the time the rocket takes to hit the ground, use the following formula for free fall when an object is launches:
where,
vo: initial velocity = 15m/s
yo: initial height = 3m
g: gravitational acceleration constant = 9.8 m/s^2
y: final height = 0 m (the rocket is on the ground)
Replace the previous values into the equation above and order the equation as a quadratic equation in standard form:
Next, use the quadratic formula, with a = 4.6, b = 15 and c = -3, to find the solutions for t:
take the positive solution for t (because negative times does not have physical meaning), then:
t = (15 + 16.85)/9.8 = 3.25 s
Hence, the rocket takes approximately 3.25 s to hit the ground