Helicopter Package Drop on Moving Target Problem

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Unit: 2D Kinematics

Prerequisites

Projectile Motion

Later Topics

None

Multi-Step Problem Preview

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Part 1

A rescue helicopter is flying horizontally at a constant altitude of $h = 291\text{ m}$ above a river, traveling at $v_{helicopter,g}= 48\text{ m/s}$ due east relative to the ground. Below, stranded hikers are on a raft drifting downstream (also due east) at $v_{raft,g} = 8\text{ m/s}$ relative to the ground.

The pilot needs to drop a supply package that will land on the raft. The package experiences projectile motion after being released (neglect air resistance, use g = 9.81 m/s²).

Determine the time of flight for the supply package from release until it reaches the water level.

Correct!

Solution:

Since the package is released from the helicopter at altitude $h = 291\text{ m}$ and falls under gravity, we can use kinematic equations for vertical motion.

The package has zero initial vertical velocity (released from a horizontally-moving helicopter), so:

$y = y_0 + v_{y0}t - \frac{1}{2}gt^2$

Taking the water level as $y = 0$ and the release point as $y_0 = h$ :

$0 = h + 0 - \frac{1}{2}gt^2$

Solving for time:

$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \cdot 291}{9.81}} = 7.7\text{ s}$

Therefore, $t_{flight} = 7.7\text{ s}$

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