The problem in the image involves an aircraft flying at a speed of 70 m/s at a height of 60 m above the ground, and a package is being dropped from the aircraft. The goal is to determine how far horizontally (denoted by $x$) from point A on the ground the package needs to be released to land at that point.

Key details:

• Horizontal velocity of the aircraft: $v = 70 \, \text{m/s}$
• Height above ground: $h = 60 \, \text{m}$
• Horizontal distance from the release point to point A: $x \, \text{(to be determined)}$

This is a typical projectile motion problem where:

• The horizontal motion is constant with velocity $v = 70 \, \text{m/s}$ since there are no forces acting horizontally (neglecting air resistance).
• The vertical motion is under the influence of gravity, so we can use the equations of motion to find the time it takes for the package to hit the ground.

Step-by-step approach:

1. Determine the time of flight using the vertical motion equation. The package is dropped from a height of $60 \, \text{m}$, and only gravity acts on it. The equation for the vertical distance under constant acceleration is:

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

   where $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$) and $t$ is the time of flight. Rearranging the equation to solve for $t$:

   $t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 60}{9.8}}$

2. Calculate the horizontal distance. Once we have the time of flight $t$, the horizontal distance $x$ can be found using:

   $x = v \times t$

Now I'll calculate the time and distance for you.The time it takes for the package to reach the ground is approximately $3.50 \, \text{seconds}$.

The horizontal distance $x$ from point A, where the package should be released, is approximately $244.95 \, \text{meters}$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How would the answer change if the plane was flying at a different altitude?
2. What happens if air resistance is considered in the calculation?
3. How would the horizontal distance change if the aircraft speed was slower?
4. Can you determine the velocity of the package just before it hits the ground?
5. How would this problem be solved if the aircraft was climbing or descending?

Tip: In projectile motion, horizontal and vertical motions are independent of each other, except that they share the same time of flight.