An Alaskan rescue plane traveling 36 m/s
drops a package of emergency rations from
a height of 137 m to a stranded party of
explorers.Where does the package strike the ground relative to the point directly below where it was released
To find out, multiply the time to fall a distance H by the plane's velocity.
X = V*t
t = sqrt(2H/g)
H = 137 m.
Solve for X
To find where the package strikes the ground relative to the point directly below where it was released, we can use the equations of motion and the fact that the only force acting on the package is gravity.
Step 1: Find the time taken for the package to reach the ground.
Using the equation of motion:
h = (1/2)gt^2
where h is the height (137 m), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Rearranging the equation, we have:
t = √((2h)/g)
Substituting in the given values:
t = √((2 * 137) / 9.8)
t ≈ √(27.959)
t ≈ 5.292 seconds
Step 2: Find the horizontal distance traveled by the package in this time.
The horizontal distance traveled by the package can be calculated using the equation:
d = v * t
where d is the horizontal distance, v is the velocity (36 m/s), and t is the time (5.292 seconds).
Substituting in the given values:
d = 36 * 5.292
d ≈ 190.512 meters.
Therefore, the package strikes the ground approximately 190.512 meters away from the point directly below where it was released.
To calculate where the package strikes the ground relative to the point directly below where it was released, we can use the equations of motion under constant acceleration.
First, we need to determine the time it takes for the package to reach the ground. We can use the equation:
s = ut + (1/2)at^2
where:
s = distance (137 m)
u = initial velocity (0 m/s, as the package is released)
a = acceleration (gravity, approximately 9.8 m/s^2)
t = time
Plugging in the values, we have:
137 = 0*t + (1/2)*9.8*t^2
Simplifying the equation:
4.9t^2 = 137
t^2 = 28
Taking the square root of both sides:
t = √28 ≈ 5.29 s
So, it would take approximately 5.29 seconds for the package to reach the ground.
Next, we can calculate the horizontal distance traveled by the plane during this time:
distance = velocity * time
distance = 36 m/s * 5.29 s ≈ 190.44 m
Therefore, the package would strike the ground approximately 190.44 meters away from the point directly below where it was released.