The important thing to note here is the direction of motion of the test rocket. Since it mentions that the rocket travels vertically upwards, then this motion can be applied to rectilinear equations that are derived from Newton's Laws of Motions.These useful equations are:
y = vāt + 1/2 atĀ²
a = (vā-vā)/t
where
y is the vertical distance travelled
vā is the initial velocity
vā is the final velocity
t is the timeĀ
a is the acceleration
When a test rocket is launched, there is an initial velocity in order to launch it to the sky. However, it would gradually reach terminal velocity in the solar system. At this point, the final velocity is equal to 0. So, vā = 0. Let's solve the second equation first.
a = (vā-vā)/t
a = (0-30)/t
a = -30/t
Let's substitute a to the first equation:
y = vāt + 1/2 atĀ²
49 = 30t + 1/2 (-30/t)tĀ²
49 = 30t -15t
49 = 15 t
t = 49/15
t = 3.27 seconds
