A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 92 m above the glacier at a speed of 135 m/s. How far short of the target should it drop the package?

How long to fall 92 m

92 = (1/2) 9.8 t^2
t = 4.333 seconds
Fly horizontal how far in 4.333 seconds:
135*4.333 = 585 meters

To find out how far short of the target the package should be dropped, we can use the equation of motion. The vertical motion equation is given by:

h = u*t + (1/2)*a*t^2

Where:
h = height (92 m above the glacier)
u = initial velocity (0 m/s since the package is dropped from rest)
a = acceleration (gravitational acceleration = -9.8 m/s^2, negative because it acts downwards)
t = time

We can rearrange the equation to solve for t:

t = √(2h / a)

Substituting the given values:

t = √(2 * 92 m / 9.8 m/s^2) ≈ 4.8 s

Now, we can find the horizontal distance covered during this time using the formula:

d = v*t

Where:
d = horizontal distance
v = horizontal velocity (given as 135 m/s)
t = time (4.8 s)

Substituting the given values:

d = 135 m/s * 4.8 s ≈ 648 m

Therefore, the supply plane should drop the package approximately 648 meters short of the target on the glacier.

To determine how far short of the target the plane should drop the package, we can use the formula for the horizontal distance traveled by an object in projectile motion.

The horizontal distance (range) can be calculated using the equation:

Range = (initial velocity x time of flight)

Since the plane is flying horizontally above the glacier, it does not have any initial vertical velocity or acceleration. Hence, the vertical component of the plane's motion does not affect the range.

First, we need to find the time of flight. The time of flight can be calculated using the equation:

Time of flight = vertical displacement / vertical component of velocity

Given that the plane flies 92 m above the glacier and has a vertical component of velocity equal to 0 m/s (since it is flying horizontally), the time of flight would be:

Time of flight = 92 m / 0 m/s

However, division by 0 is undefined, and we cannot determine the time of flight in this case. This means the package will never reach the scientists.

Therefore, the plane should not drop the package at all, as it will fall short of the target. Perhaps an alternative method of delivery or approach needs to be considered to deliver the package to the scientists successfully.

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