On a day with a breeze blowing from the west at 8.5km/h, a remote control helicopter, facing north, takes off vertically from a level field at full power. It has a mass of 700g and the propeller generates 10N of thrust when running at full power. Once it reaches a height of 5m, the helicopter is tilted forward so that it maintains its height and accelerates towards the north. 10s later, the helicopter collides with a tree. How far away and in what direction is the tree from the place where the helicopter took off?

On a day with a breeze blowing from the west at 8.5km/h, a remote control helicopter, facing north, takes off vertically from a level field at full power. It has a mass of 700g and the propeller generates 10N of thrust when running at full power. Once it reaches a height of 5m, the helicopter is tilted forward so that it maintains its height and accelerates towards the north. 10s later, the helicopter collides with a tree. How far away and in what direction is the tree from the place where the helicopter took off?

To determine the distance and direction of the tree from the place where the helicopter took off, we need to break down the problem into different stages and analyze each stage step by step:

Stage 1: Vertical Ascent
First, let's calculate the time it takes for the helicopter to reach a height of 5m:
We can use the equation of motion: distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Where distance = 5m, initial velocity = 0 m/s, and acceleration = 10N (thrust) / mass (0.7 kg)
Using the rearranged equation: time = sqrt((2 * distance) / acceleration), we can calculate the time it takes for the vertical ascent.

Stage 2: Horizontal Movement
After reaching a height of 5m, the helicopter tilts forward and accelerates towards the north. To determine its velocity in the north direction, we need to calculate the acceleration first.

The only force acting in the northward direction is the horizontal component of the propeller's thrust. To calculate this force, we can use trignometry:
Force north = thrust * sin(angle of tilt)
The angle of tilt can be determined using trigonometry as well, knowing that the helicopter is facing north and the wind is blowing from the west.

Now, we can calculate the acceleration using Newton's second law of motion: acceleration = Force north / mass.

With the acceleration known, we can proceed to determine the helicopter's velocity in the northward direction after 10 seconds using the formula: final velocity = initial velocity + (acceleration * time)

Stage 3: Collision with the Tree
Finally, once we have the final northward velocity, we can calculate the distance traveled by the helicopter towards the north: distance = velocity * time.

Combining all the information obtained from the calculations, we can determine the distance and direction of the tree from the place where the helicopter took off.

Note: Some additional assumptions were made for the calculations, such as ignoring air resistance and assuming a constant thrust throughout the flight. Real-life scenarios may involve more complexities.