Question

An instrument is thrown upward with a speed of 15 m/s on the surface of planet X where the acceleration due to gravity is 2.5 m/s2 and there is no atmosphere. How long does it take for the instrument to return to where it was thrown?

Answer 1

Answer: 12 s

Explanation:

The situation described here is parabolic movement. However, as we are told the instrument is thrown upward from the surface, we will only use the equations related to the Y axis.

In this sense, the main movement equation in the Y axis is:

$y-y_{o}=V_{o}.t-\frac{1}{2}g.t^{2}$    (1)

Where:

$y$  is the instrument's final position  

$y_{o}=0$  is the instrument's initial position

$V_{o}=15m/s$ is the instrument's initial velocity

$t$ is the time the parabolic movement lasts

$g=2.5\frac{m}{s^{2}}$  is the acceleration due to gravity at the surface of planet X.

As we know $y_{o}=0$  and $y=0$ when the object hits the ground, equation (1) is rewritten as:

$0=V_{o}.t-\frac{1}{2}g.t^{2}$    (2)

Finding $t$:

$0=t(V_{o}-\frac{1}{2}g.t^{2})$   (3)

$t=\frac{2V_{o}}{g}$   (4)

$t=\frac{2(15m/s)}{2.5\frac{m}{s^{2}}}$   (5)

Finally:

$t=12s$