"Special Topic Strengthening Application of the Laws of Flat Throwing Motion" Excellent Courseware of Projectile Motion PPT

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"Special Topic Strengthening Application of the Laws of Flat Throwing Motion" Excellent Courseware of Projectile Motion PPT

Part One: Learning Objectives

1. Be able to skillfully use the laws of flat throwing motion to solve problems.

2. Be able to analyze the problem of combining flat throwing motion with other motions.

3. Be able to analyze motions similar to flat throws.

Special PPT on strengthening the application of the laws of flat throwing motion, part 2 content: 01 Exploring key points to improve literacy

1. Two important corollaries and applications of flat throwing motion

1. The reverse extension line of the instantaneous velocity of an object in horizontal motion at any moment must pass through the midpoint of the horizontal displacement at that time.

2. The relationship between the angles θ and α between the velocity direction, displacement direction and the initial velocity direction of an object in horizontal motion at a certain moment is tan θ = 2tan α.

Example 1 As shown in Figure 1, if the top of an object with a fixed inclination angle of θ is thrown in the horizontal direction and still lands on the incline, then the angle φ between the speed of the object and the horizontal direction when it comes into contact with the incline satisfies (air resistance is not considered)

A.tan φ＝sin θ

B.tan φ＝cos θ

C.tan φ＝tan θ

D.tan φ＝2tan θ

2. Flat throwing motion related to inclined plane

The characteristics and analysis methods of the flat throwing motion related to the inclined plane are as follows:

Example 2 (End of the first semester of Changfeng No. 2 Middle School, 2019) As shown in Figure 2, an inclined plane with an inclination angle of 37° is fixed on the horizontal plane. A small ball is moved at the O point directly above the bottom of the inclined plane at a speed of v0 = 3 m/s. Throw it horizontally. After a period of time, the ball hits point P on the slope vertically. (The ball can be regarded as a mass point, regardless of air resistance. Take the acceleration of gravity g = 10 m/s2, sin 37° = 0.6, cos 37° =0.8), then

A. The speed of the ball when it hits the slope is 5 m/s

B. The speed of the ball when it hits the slope is 4 m/s

C. The horizontal displacement of the ball when it is thrown horizontally is 1.6 m

D. The vertical displacement of the ball when it is thrown horizontally is 1 m

Summary and improvement

In Example 2, the object falls vertically on the slope, and the terminal velocity direction is known. Generally, the terminal velocity of the object is decomposed, and the relationship between the two velocity is determined by the velocity direction.

Example 3 As shown in Figure 3, AB is a fixed slope with an inclination angle of 30°. The ball is thrown horizontally from point A with an initial velocity v0 and falls exactly at point B. Find: (Ignoring air resistance, the acceleration due to gravity is g)

(1) The distance between A and B and the time the ball flies in the air;

(2) From the time it was thrown, how long did it take for the distance between the ball and the inclined plane to be the largest? What is the maximum distance?

Summary and improvement

1. After the object is thrown from the inclined plane and then falls on the inclined plane, the displacement direction is known. Generally, the displacement is decomposed, and the relationship between the two displacements is determined by the displacement direction.

2. The motion of the object in Example 3 satisfies the following rules:

(1) The ratio of the vertical displacement to the horizontal displacement of an object is a constant, which is equal to the tangent of the inclination angle of the incline;

(2) The movement time of an object is proportional to the initial velocity;

(3) When an object falls on an inclined plane, the displacement direction is the same, along the inclined plane;

(4) The speed directions of objects falling on different positions on the slope are parallel to each other;

(5) When the object’s velocity direction is parallel to the incline, the distance from the object to the incline is maximum.

3. Flat throwing motion

Throw-like motion refers to the curved motion of an object. Its motion can be decomposed into two mutually perpendicular sub-movements: one direction is uniform linear motion, and the other direction is uniform motion with an initial velocity of zero under the action of a constant external force. Accelerate linear motion.

(1) Force characteristics of flat throwing motion

The net external force on the object is a constant force and is perpendicular to the direction of the initial velocity.

(2) Movement rules of similar flat throwing motion

In the direction of initial velocity v0: vx=v0, x=v0t.

Example 4 As shown in Figure 5, the length of the smooth fixed inclined plane is l, the width is b, and the inclination angle is θ. A block (can be regarded as a particle) is incident horizontally along the upper left vertex P of the inclined plane and leaves the inclined plane exactly from the bottom point Q. , try to find: (gravitational acceleration is g, not counting air resistance)

(1) The time t takes for the block to move from P to Q;

(2) The initial velocity v0 of the block when it is shot horizontally from point P;

(3) The speed v of the block when it leaves point Q.

Special PPT on strengthening the application of the laws of flat throwing motion, the third part of the content: 02 in-class drills, implementation point by point

1. (Flat throwing motion related to the inclined plane) (2018·National Volume III) At the top of an inclined plane, two small balls A and B are thrown horizontally in the same direction at the speed of v and respectively. Both balls land on the On an incline. The velocity of ball A when it falls on the incline is the velocity of ball B when it falls on the incline.

A.2 times B.4 times C.6 times D.8 times

2. (Flat throwing motion related to the inclined plane) (Multiple choice) (2018·Leshan City High School Inspection) As shown in Figure 6, the inclination angle of a fixed inclined plane is θ, and the ball A is moved horizontally to the right from the top of the inclined plane at a speed v0 Throw it and hit point P on the incline. Ball B is thrown horizontally to the left from a certain point in the air at the same speed v0. It happens to hit point Q on the vertical incline. Ignoring air resistance, the acceleration due to gravity is g. The following statement is correct yes

A. If the acute angle between the speed direction and the horizontal direction of ball A when it hits point P is φ, then tan θ=2tan φ

B. If the acute angle between the speed direction and the horizontal direction of ball A when it hits point P is φ, then tan φ=2tan θ

C. The ratio of the time that balls A and B move in the air is 2tan2 θ:1

D. The ratio of the time that balls A and B move in the air is tan2 θ:1

3. (Inference of the law of horizontal throwing motion) As shown in Figure 7, the same small ball is thrown horizontally at different initial velocities from a certain point on the inclined plane with an inclination angle of θ. The small balls all land on the inclined plane. When thrown When the speed of the ball is v1, the angle between the speed direction and the slope when the ball reaches the slope is α1; when the throwing speed is v2, the angle between the speed direction and the slope when the ball reaches the slope is α2, excluding air resistance, then

A. When v1>v2, α1>α2

B. When v1>v2, α1<α2

C. Regardless of the relationship between v1 and v2, α1=α2

D.The relationship between α1 and α2 is related to the inclination angle θ of the incline

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"Special Topic Strengthening the Application of the Laws of Flat Throwing Motion" Projectile Motion PPT High-Quality Courseware:

"Special Topic Strengthening the Application of the Laws of Flat Throwing Motion" Projectile Motion PPT High-Quality Courseware Knowledge Expansion Point - Two Inferences of Flat Throwing Motion Corollary 1: Starting from the throwing point, the tangent of the velocity deflection angle at any time is equal to the tangent of the displacement deflection angle 2 times the value, as shown in the figure..

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Update Time: 2024-09-04

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