A helicopter is ascending vertically with a speed of 5.32 m/s . At a height of 120 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [Hint: What is v0 for the package?]

Approximately (assuming that .)

Explanation:

From the perspective of an observer on the ground, the package was initially moving with the helicopter. The initial velocity of that package () would be the same as the velocity of the helicopter. In other words, .

Other quantities:

There are two ways to find the time required for the package to reach the ground after it was dropped.

The first approach makes use of the SUVAT equation:

.

For this question, , , and are already known. However, this approach would require solving a quadratic equation where the coefficient for the first-order term is non-zero.

An alternative approach is to solve for , the velocity of the package right before it reaches the ground. From the SUVAT equation that does involve time:

.

Again, , , and are already known. Solve for :

.

Calculate time from the change in velocity:

.

no. dot product   =0 when vecs at right angles