Amazon is bringing me a box of shark repellent to my small island (about a 10 m diameter). They are going to drop it as they fly overhead. The plane flies 125 m above the ground at a speed of 550 m/s. How far away from my island should they drop my supplies so that it lands on the island?

I'm confused on how to go about solving this problem. Could someone help explain this?

how long does it take to fall 125 meters?

4.9t^2 = 125

Using that value of t, how far will the package move at 550 m/s ? You might want to consider an extra 5 meters to hit at the center of the island?

Okay so if I found t=5.04 s, then all I need to do is use d=speed*time?

d=550*5.04= 2772 meters

or if I add an extra 5 meters:
d=555*5.04=2792.2 meters

Did I do that right?

You should subtract the 5 meters from the calculated distance, or the package will land 5 meters from shore in the water, rather than on land!

2772 - 5 = 2767

You added an extra 5 m/s to the speed!

Certainly! To solve this problem, we can use the concept of projectile motion and the equations of motion.

First, let's break down the problem. We want to find the horizontal distance that the supplies need to be dropped so that it lands on your island. The supplies will be dropped from a plane flying at a height of 125 m above the ground. The plane's speed is given as 550 m/s.

Since we are only interested in the horizontal distance, we can ignore the vertical motion. This means we can treat the problem as a 2-dimensional motion in the x-direction.

To solve for the horizontal distance, we can use the equation:

distance = speed * time

In this case, the distance is the horizontal distance from the plane to your island. The speed is the speed of the plane, which is given as 550 m/s. The time is the time it takes for the supplies to fall from the plane to the ground.

To find the time, we can use the equation:

time = height / (acceleration due to gravity)

The height is the height of the plane above the ground, which is given as 125 m. The acceleration due to gravity is a constant value of approximately 9.8 m/s^2 on Earth.

Now, let's substitute the given values into the equations:

time = 125 m / 9.8 m/s^2
time ≈ 12.76 s

Now that we have the time, we can find the horizontal distance by multiplying the speed of the plane by the time:

distance = 550 m/s * 12.76 s
distance ≈ 7028 m

Therefore, the supplies should be dropped approximately 7028 meters away from your island so that it lands on the island.