# 1D Motion homework

A helicopter is ascending vertically with a speed of 4.00 m/s. At a height of 125 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground? [Hint: The package's initial speed equals the helicopter's.]

So using the displacement formula $x=x_0 + v_0t + (1/2)at^2$, I did $-4.9t^2 - 4t + 125 =0$ at first, because the package was travelling downwards and so its initial velocity would be negative. However, instead, solving $-4.9t^2 +​4t + 125 =0$ returned the correct answer (I just fit in the equation using the hint). But I don't understand why then the initial velocity of the falling package would be $4.00m/s$, not a negative value.

• Isn't the package initially moving upward relative to the ground? – Bill N Sep 8 '17 at 21:27

## 2 Answers

There's a typo, the equation you want to solve is $-4.9t^2+4t+125=0$.

Since the initial velocity and acceleration have an opposite direction, they must have different sign

As you have put the acceleration, which acts downwards, as negative. This means up is positive. The initial velocity of the package is 4m/s upwards (as the helicopter was ascending vertically) so it will be positive.