A drone capable of flying north at a speed of 4.0 m/s in still air is attempting to fly across a field 120 m wide. There is a wind blowing at 5.0 m/s [E].

a) Find the drone's velocity relative to the ground.

b) Find the time it takes the drone to cross the field.

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X = 5m/s. = Vw.

Y = 4 m/s = Vd.

a. Tan A = Y/X = 4/5 = 0.8, A = 38.7o. N. of E. = 51.3o E. of N.
Vr = X/Cos A=5/Cos38.7=6.4 m/s[38.7o] = Resultant drone velocity.

b. d = 120/sin38.7 = 192 m. To cross the
field.

V*t = 192, 4*t = 192, t = 48 s.

To find the drone's velocity relative to the ground, we need to consider the velocity of both the drone and the wind.

a) The drone's velocity relative to the ground can be found by subtracting the wind's velocity from the drone's velocity. In this case, the drone is flying north at a speed of 4.0 m/s, and the wind is blowing east at a speed of 5.0 m/s.

Since the drone's motion is perpendicular to the wind, we can use the Pythagorean theorem to find the resultant velocity. The resultant velocity is the magnitude of the vector formed by adding the drone's velocity and the wind's velocity.

Using the Pythagorean theorem, we have:

Resultant velocity^2 = (drone's velocity)^2 + (wind's velocity)^2
Resultant velocity^2 = (4.0 m/s)^2 + (5.0 m/s)^2
Resultant velocity^2 = 16.0 m^2/s^2 + 25.0 m^2/s^2
Resultant velocity^2 = 41.0 m^2/s^2

Taking the square root of both sides, we find:

Resultant velocity = √(41.0 m^2/s^2)
Resultant velocity ≈ 6.4 m/s

Therefore, the drone's velocity relative to the ground is approximately 6.4 m/s.

b) To find the time it takes the drone to cross the field, we can use the formula distance = speed × time.

The drone needs to cross a field that is 120 m wide. Since the drone's velocity relative to the ground is 6.4 m/s, we can write:

120 m = 6.4 m/s × time

Now we can solve for time:

time = 120 m / 6.4 m/s
time ≈ 18.75 s

Therefore, it takes approximately 18.75 seconds for the drone to cross the field.