A plane needs to drop supplies off to victims of natural disasters around the world. The first stop is for flood victims but they must drop the box so it lands perfectly on a target. If they are flying at 191 m/s and are 84.0 m above the ground, what distance before the target should they drop the package?
To find the distance before the target at which the package should be dropped, we need to consider the horizontal motion of the plane and the vertical motion of the package.
Let's break down the problem into two components: horizontal and vertical.
1. Horizontal Motion:
Since there is no horizontal acceleration, the horizontal speed of the plane will remain constant throughout the motion. The distance traveled horizontally is given by the formula:
Distance = Speed × Time
We need to find the time it takes for the package to reach the target. Since the horizontal speed of the plane and the speed of the package are the same, we can use the time taken by the plane to calculate the horizontal distance:
Time = Distance / Speed
Given that the speed of the plane is 191 m/s, we can use this speed to calculate the time it takes for the plane to reach the target.
2. Vertical Motion:
The vertical motion of the package is influenced by gravity. We need to calculate the time it takes for the package to fall from a height of 84.0 m to the ground.
The formula to calculate the time for an object to fall from a height h (assuming no air resistance) is given by:
h = (1/2) * g * t^2
Where:
h = height = 84.0 m
g = acceleration due to gravity = 9.8 m/s^2
t = time
We can rearrange the equation to solve for time:
t = sqrt(2 * h / g)
Now, we have the time it takes for the package to fall from the plane to the ground.
3. Total Distance:
To find the distance before the target at which the package should be dropped, we need to multiply the time taken by the plane to reach the target by the horizontal speed of the plane:
Total Distance = Time * Speed
Calculating the values:
1. Time: Time = Distance / Speed
2. Time for vertical motion: t = sqrt(2 * h / g)
3. Total Distance: Total Distance = Time * Speed
Now, plug in the given values and calculate step by step to find the distance before the target at which the package should be dropped.
time to fall 84m
84=1/2 g t^2
t=sqrt(168/9.8)
distance=191*timeabove