The helicopter flies horizontally at a speed of 180. Control physics

A helicopter flies at an altitude of 500 m at a speed of 100 m/s. A boat is moving towards him along the river at a speed of 20 m/s, onto which a load is being dropped from a helicopter. How far away from the boat should the helicopter be when releasing its cargo?

Problem No. 1.7.20 from the “Collection of problems for preparing for entrance exams in physics USPTU"

Given:

\(H=500\) m, \(\upsilon_1=100\) m/s, \(\upsilon_2=20\) m/s, \(L-?\)

Solution to the problem:

The first thing I would like to say is that at the moment the load is released, its speed is equal in magnitude and direction to the speed of the helicopter.

Since in the problem we are dealing with relative motion, we will move to the reference frame (FR) of the boat. To determine the speed vector of the load \(\overrightarrow ((\upsilon _(21)))\) in this reference frame, it is necessary to add to the vector of its speed relative to the Earth \(\overrightarrow ((\upsilon _1))\) a vector equal in magnitude and opposite in direction to the speed vector of the boat (\(— \overrightarrow ((\upsilon _2))\)).

Since the load and the boat are moving towards each other, the modulus of the vector \(\overrightarrow ((\upsilon _(21)))\) is equal to:

\[(\upsilon _(21)) = (\upsilon _1) + (\upsilon _2)\]

Let's write down the equations of motion of the load in projections on the \(x\) and \(y\) axes.

\[\left\( \begin(gathered)
ox:x = (\upsilon _(21))t \hfill \\
oy:y = \frac((g(t^2)))(2) \hfill \\
\end(gathered) \right.\]

When the load falls on the boat, it will travel a horizontal distance \(L\), and a vertical distance \(H\).

\[\left\( \begin(gathered)
L = (\upsilon _(21))t \;\;\;\;(1)\hfill \\
H = \frac((g(t^2)))(2) \;\;\;\;(2)\hfill \\
\end(gathered) \right.\]

From expression (2) we find the fall time:

Let us substitute the previously obtained expressions into formula (1) to obtain the final formula.

Answer: 1.2 km.

If you do not understand the solution and you have any questions or you have found an error, then feel free to leave a comment below.

Test in physics Free fall. Ballistic movement grade 10 with answers. The test includes 4 options, each option has 6 tasks.

1 option

1. The body fell from a height of 45 m. What is the time of fall of the body?

2. A boy threw a ball horizontally from a window at a height of 20 m. Determine at what speed the ball was thrown if it fell 6 m from the base of the house.

3. The boy threw the ball vertically upward and caught it after 2 seconds. What is the maximum height the ball rose to?

4. A stone thrown horizontally from a height of 2 m above the ground falls at a distance of 7 m. Find the initial and final velocities of the ball.

5. A body thrown vertically upward from the surface of the earth at a speed of 30 m/s twice reached a height of 40 m. What period of time separates these two events?

6. A body is thrown at an angle of 60° to the horizontal with an initial speed of 30 m/s. At what altitude will the velocity vector make an angle of 45° with the horizon?

Option 2

1. Find the speed with which the body will fall to the surface of the earth if it falls freely from a height of 5 m.

2. The bullet is fired horizontally and travels at a speed of 800 m/s. How much will the bullet drop in a vertical direction during flight if the distance to the target is 600 m?

3. At what speed did the ball fly out of the spring pistol if after the shot it rose to a height of 5 m?

4. A stone is thrown at an angle of 30° to the horizontal with a speed of 10 m/s. How long will it take for him to reach a height of 1 m?

5. A free-falling stone travels the last three-quarters of the way in 1 s. From what height did the stone fall?

6. The helicopter flies horizontally at a speed of 180 km/h at an altitude of 500 m. From the helicopter onto the motor ship you need to drop a pennant moving on a counter course at a speed of 24 km/h. At what distance from the ship should the pilot drop the pennant?

Option 3

1. What is it equal to maximum height, to which a body thrown vertically upward at a speed of 40 m/s will rise?

2. The gun is positioned horizontally at a height of 3 m above the ground. How long after the shot does the bullet hit the ground?

3. What is the initial speed of an arrow shot vertically from a bow if it hits the ground after 6 s?

4. The flight range of a body thrown horizontally at a speed of 10 m/s is equal to the height of the throw. From what height was the body dropped?

5. A freely falling body traveled the last 30 m in a time of 0.5 s. Find the height from which the body fell.

6. A ball thrown by one player to another at an angle to the horizontal at a speed of 20 m/s reaches its highest point in 1 s. How far were the players from each other?

Option 4

1. Calculate the time during which the stone, which began to fall freely, will go the way 20 m.

2. A load is dropped from a helicopter moving horizontally at a speed of 40 m/s at an altitude of 500 m without an initial velocity relative to the helicopter. At what horizontal distance from the point of release will the load fall?

3. How many times must the initial speed of a body thrown upward be increased so that the maximum lift height increases by 4 times?

4. A boy dives into water from a steep bank 5 m high, having a horizontal speed of 6 m/s after the run. What is the magnitude and direction of the boy's velocity when he reaches the surface of the water?

5. An icicle falls from the roof of a house. She flew the first half of the journey in 1 s. How much time does she have left to fly?

6. The plane flies horizontally at an altitude of 8 km at a speed of 1800 km/h. How many kilometers from the target must the pilot drop the bomb to hit the target?

ANSWERS - Physics test Free fall. Ballistic movement grade 10
1 option
1.3 s
2. 3 m/s
3.5 m
4. 11 m/s, 13 m/s
5. 2 s
6. 21.3 m
Option 2
1. 10 m/s
2. 2.8 m
3. 10 m/s
4. 0.28 s, 0.74 s
5. 20 m
6. 570 m
Option 3
1. 80 m
2. 0.8 s
3. 30 m/s
4. 20 m
5. 195 m
6. 34.6 m
Option 4
1.2 s
2. 400 m
3. 2 times
4. 11.7 m/s, 59° to the horizon
5. 0.41 s
6. 20 km

A disk with a radius of 20 cm rotates uniformly around its axis. The speed of a point located at a distance of 15 cm from the center of the disk is 1.5 m/s. The speed of the extreme points of the disk is equal to?

A small stone thrown from a flat horizontal surface of the earth at an angle to the horizon fell back to the ground 20 m from the time of the throw. How much time passed from the throw to the moment when its speed was directed horizontally and equal to 10 m/s?

Two gears meshed with each other rotate around fixed axes (see figure). The ratio of the rotation periods of the gears is 3. The radius of the smaller gear is 6 cm. What is the radius of the larger gear?

During the first 3 s, the elevator cage rises uniformly and reaches a speed of 3 m/s, with which the rise continues for 6 s. During the last 3 seconds of braking, it moves with the initial acceleration. Determine the height.

Find the extension of a steel spring 50 cm long, to the end of which a ball weighing 100 g is attached, if it rotates at 60 rpm. Spring stiffness 13000 N/m.

Option 2

A space rocket accelerates from rest and, having covered a path of 200 km, reaches a speed of 11 km/s. How fast was she moving? What is the acceleration time?

An airplane flying horizontally at an altitude of 500 m at a constant speed of 300 m/s drops a bomb on a stationary target. At what horizontal distance to the target must the bomb be dropped in order for it to hit the target?

The body is free from a height of 80 m. What is its displacement at the last second of the fall?

The shaft makes 1440 rpm. Determine the period of rotation of the pulley mounted on the shaft, the angular and linear speed of the points on its rim. If the pulley diameter is 0.4 m.