An airplane traveling 1015 m above the ocean at 115 km/h is going to drop a box of supplies to shipwrecked victims below.

(a) How many seconds before the plane is directly overhead should the box be dropped?

(b) What is the horizontal distance between the plane and the victims when the box is dropped?

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To solve these problems, we can use the equations of motion and the concept of relative velocities. Here's how to solve them step by step:

(a) How many seconds before the plane is directly overhead should the box be dropped?

To solve this, we need to find the time it takes for the box to fall from the airplane to the victims below.

Step 1: Convert the altitude from meters to kilometers.
The altitude is given as 1015 meters. Since the horizontal distance is provided in kilometers, it's beneficial to convert the altitude to kilometers as well. 1 kilometer = 1000 meters, so the altitude is 1015 / 1000 = 1.015 kilometers.

Step 2: Calculate the time for the box to fall.
The time it takes for an object to fall can be found using the equation:

Time = √(2h / g),

where h is the height (altitude) and g is the acceleration due to gravity (approximately 9.8 m/s²).

Using this equation, we can plug in the values:

Time = √(2 * 1.015 / 9.8) seconds.

Calculating this expression gives us the time it takes for the box to fall.

(b) What is the horizontal distance between the plane and the victims when the box is dropped?

To find the horizontal distance, we need to multiply the speed of the airplane by the time it takes for the box to fall.

Step 1: Convert the speed from km/h to m/s.
The speed is given as 115 km/h. To convert it to m/s, divide it by 3.6 (1 km/h = 1000 m/3600 s = 1/3.6 m/s).

Speed = 115 / 3.6 m/s.

Step 2: Calculate the horizontal distance.
The horizontal distance is given by the equation:

Distance = Speed * Time.

Using the values we obtained earlier, we can plug them into the equation and calculate the distance.

This will give us the horizontal distance between the plane and the victims when the box is dropped.

a) I will let you figure out how long an object takes to drop 1015 meters.

1015 = (1/2) g t^2

b) LOL