Question

13. A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 150 m/s. How far short of the target should it drop the package?

Short answer

The package is required to drop at short distance $680\text{m}$from the target

Step-by-step solution

Step 1. Given information

The plane flies the distancea $100\text{m}$above the ground at a speed of $150\text{m}/\text{s}$.

The following figure shows the motion of the package drop from a plane.

Step 2. Explanation

The height at which the package is dropped is,

$h=u_{y}t+\frac{1}{2}g{t}^2$

Here, h is the vertical height, $u_y$is the initial velocity of the package, and g is the acceleration due to gravity.

$\begin{array}{l}(100\text{m})=(0\text{m}/\text{s})t+\frac{1}{2}(9.8\text{m}/\text{s})t^2\\ \frac{1}{2}(9.8\text{m}/\text{s})t^2=(100\text{m})\\ t=\sqrt{20.48}\\ =4.52\text{s}\end{array}$

Thus, the travel period of the package is $4.52\text{s}$.

The horizontal distance traveled by the package is $D=vt\left(\text{I}\right)$

$\begin{array}{l}D=(150\text{m}/\text{s})(4.52\text{s})\\ =678\text{m}\\ \approx 680\text{m}\end{array}$

Therefore, the package is required to drop at $680\text{m}$short distance of the target.