A helicopter is flying horizontally at 7.52 m/s and an altitude of 16.6 m when a package of emergency medical supplies is ejected horizontally backward with a speed of 11.9 m/s relative to the helicopter. Ignoring air resistance, what is the horizontal distance between the package and the helicopter when the package hits the ground?
I will be happy to critique your thinking.
To solve this problem, we can use the principles of projectile motion. We need to find the horizontal distance traveled by the package when it hits the ground, assuming no air resistance. Here are the steps to solve the problem:
Step 1: Analyze the vertical motion of the package
Since the package is ejected horizontally, the initial vertical velocity is zero. The only thing affecting the vertical motion is gravity. We can use the following equation to find the time it takes for the package to hit the ground:
h = (1/2) * g * t^2
Where:
h = initial vertical displacement (altitude)
g = acceleration due to gravity (9.8 m/s^2)
t = time
Substituting the known values, we can solve for t:
16.6 = (1/2) * 9.8 * t^2
Step 2: Calculate the time of flight
Solving the above equation for t, we find:
t = sqrt(2h / g)
t = sqrt(2 * 16.6 / 9.8) = 2.05 s
Therefore, it takes approximately 2.05 seconds for the package to hit the ground.
Step 3: Calculate the horizontal distance traveled by the package
To find the horizontal distance traveled by the package, we can use:
d = v * t
Where:
d = horizontal distance
v = horizontal velocity (relative to the helicopter)
t = time of flight
Substituting the known values:
d = 7.52 m/s * 2.05 s
d = 15.396 m
Therefore, the horizontal distance between the package and the helicopter when the package hits the ground is approximately 15.396 meters.