A rescue helicopter drops a package of emergency ration to a stranded party on the ground. If the helicopter is travelling horizontally at 40m/s at a height of 100m above the ground, what are the horizontal and vertical component of the velocity of the package just before it hits the ground?

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A rescue helicopter drops a package of emergency ration to a stranded party on the ground. If the helicopter is travelling horizontally at 40m/s at a height of 100m above the ground, what are the horizontal and vertical component of the velocity of the package just before it hits the ground?

a rescue plane flying horizontally at 175 km/h [N], at an altitude of 150 m, drops a 25kg emergency package to a group of explorers. Where will the package land relative to the point above which it was released. (Neglect friction)

To find the horizontal and vertical components of the velocity of the package just before it hits the ground, we can use the fact that the horizontal component of the velocity remains constant, while the vertical component changes due to the effects of gravity.

First, let's find the time it takes for the package to reach the ground. We can use the equation of motion in the vertical direction:

h = v_i * t + (1/2) * g * t^2

Where:
h is the height of the helicopter above the ground (100m),
v_i is the initial vertical velocity (which we are looking for),
t is the time taken to reach the ground (which we want to find), and
g is the acceleration due to gravity (-9.8 m/s^2).

Since the package is dropped (not thrown upward or downward), the initial vertical velocity (v_i) is zero. Thus, the equation simplifies to:

h = (1/2) * g * t^2

Solving for t:

t = sqrt((2h) / g)
= sqrt((2 * 100) / 9.8)
≈ 4.52 seconds

Now that we have the time, we can find the vertical component of the velocity just before the package hits the ground using the equation of motion:

v_f = v_i + g * t

v_f = 0 + (-9.8) * 4.52
≈ -44.3 m/s

Note that the negative sign indicates that the velocity is directed downward.

Finally, since the horizontal component of the velocity remains constant at 40 m/s, the horizontal component just before the package hits the ground is also 40 m/s.

Therefore, the horizontal component of the velocity is 40 m/s, and the vertical component of the velocity is approximately -44.3 m/s.