A plane drops a package of emergency rations to a stranded party of explorers the plane is traveling horizontally at 40m/s at a height of 100m from the ground find where the package strikes the ground ralative to the spot where it was dropped
Multiply the time to drop 100 m by the horizontal velocity of the airplane.
fist you take 100 and then *2 to get 200 then do3.275 * 40 and get 131 then all you need to do is 200-131... and get______________________________________________
To find where the package strikes the ground relative to the spot where it was dropped, we need to determine the horizontal distance traveled by the package.
First, we can calculate the time it takes for the package to reach the ground. We will use the equation for free fall motion:
h = (1/2) * g * t^2
Where:
h = height = 100m
g = acceleration due to gravity = 9.8m/s^2
Rearranging the equation to solve for time (t), we have:
t = √(2 * h / g)
Substituting the given values, we have:
t = √(2 * 100 / 9.8)
t ≈ √(20.41)
t ≈ 4.52s
Now that we know the time it takes for the package to reach the ground, we can find the horizontal distance traveled by multiplying the horizontal velocity of the plane (40m/s) by the time (4.52s):
Distance = Velocity * Time
Distance = 40m/s * 4.52s
Distance ≈ 180.8m
Therefore, the package strikes the ground approximately 180.8m horizontally from the spot where it was dropped.
To find where the package strikes the ground relative to the spot it was dropped, we need to use the equations of motion and the concept of projectile motion.
1. First, let's analyze the horizontal motion of the package. The plane is traveling horizontally at a speed of 40 m/s, and we can assume that there is no horizontal acceleration. Therefore, the horizontal distance traveled by the package is given by:
Distance (horizontal) = Speed (horizontal) × Time (horizontal)
Since the package is dropped vertically, its horizontal speed remains constant throughout. So, we can find the time it takes for the package to reach the ground by using the height and gravitational acceleration.
2. Now, let's analyze the vertical motion of the package. The package is dropped from a height of 100m, and we can assume that there is no initial vertical velocity. The only force acting on it is gravity, causing it to accelerate downwards. Therefore, we can use the equation of motion:
Final vertical position = Initial vertical position + Initial vertical velocity × Time (vertical) + 0.5 × Acceleration (vertical) × Time (vertical)^2
The final vertical position will be the height above the ground where the package strikes, the initial vertical position will be 100m, the initial vertical velocity will be 0 m/s, and the acceleration will be gravitational acceleration (approximately 9.8 m/s^2).
3. Now, we can combine the horizontal and vertical motion to find the point where the package strikes the ground relative to the spot it was dropped. The horizontal distance traveled will give us the relative position.
To summarize the steps:
a. Calculate the time taken to reach the ground using the vertical motion.
b. Multiply the time obtained in (a) with the horizontal speed to get the horizontal distance traveled.
Note: In this calculation, we are assuming ideal conditions without considering air resistance.