Horizontal Motion Questions

Horizontal motion is defined as projectile motion in a horizontal plane caused by a force.

• When a particle is thrown obliquely near the surface of the earth, it follows a curved, constant acceleration path to the center of the earth. 
• The path of such a particle is called a projectile, and its motion is called projectile motion.
• The projectile motion is divided into two components: horizontal motion and vertical motion.
• A projectile must be thrown in a straight line, not at an angle, to achieve horizontal motion. 
• The velocity of the projectile changes, but the direction in which it is fired should be perpendicular to the Earth's surface.
• As the projectile is launched, a constant vertical force of gravity acts upon it, which is independent of the horizontal force.

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Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following is not an example of motion in a plane?

1. A bicycle moving in a circular path
2. A truck moving in an infinite spiral
3. A rocket moving into space
4. A car moving in a rectangular path

Ans. The correct answer is c. A rocket moving into space

Explanation: A rocket in space is an example of three-dimensional motion. Therefore, it cannot come under the category of motion in a plane. Rest all the options are examples of motion in a plane.

Ques. Which of the following is not true about projectile motion?

1. The acceleration keeps changing in projectile motion
2. It is an example of motion along a curve
3. It is an example of motion in a plane
4. It is not an example of motion in space

Ans. The correct answer is a. The acceleration keeps changing in projectile motion

Explanation: The only acceleration in projectile motion is acceleration due to gravity. If the top height of the projectile motion is small and can be ignored in relation to the radius of the earth, the acceleration caused by gravity remains constant. Therefore, in projectile motion, the acceleration remains constant.

Ques. A body is exhibiting circular motion. What kind of motion can this be?

1. Motion in space
2. Motion in a plane
3. Motion along a point
4. Motion along a line

Ans. The correct answer is b. Motion in a plane

Explanation: Circular motion is an example of motion in a plane. Because a circle is a two-dimensional object, a moving body in a circle is also traveling on a plane. As a result, the motion may be described as motion in a plane.

Ques. On calculating which of the following quantities, the mass of the body has an effect in simple projectile motion?

1. Time of flight
2. Force
3. Velocity
4. Range

Ans. The correct answer is b. Force

Explanation: Except for force, all of the quantities stated are kinematic quantities. Force is a type of kinetic quantity. Force acting on a body is given by the product of mass and acceleration of the body. As a result, the mass of the body influences force calculation.

Ques. How many variables are required to define the motion of a body in a plane?

1. 1
2. 2
3. 3
4. 4

Ans. The correct answer is b. 2

Explanation: Two variables can be used to define the motion of a body in a plane. 

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Short Answers Questions [2 Marks Questions]

Ques. Define Horizontal motion.

Ans. Horizontal motion is defined as projectile motion in a horizontal plane caused by a force. The vertical and horizontal components of a projectile are perpendicular and independent of each other for a short distance.

Ques. What are the examples of horizontal motion?

Ans. A few examples of horizontal motion are

• The motion of a boat in a river.
• Throwing a ball or a cannonball.
• The motion of the billiard ball on the billiard table.
• A bullet fired from a gun.
• The motion of the planet Earth around the Sun.

Ques. Define Verticle motion.

Ans. Vertical motion occurs when we throw an object totally up, which means that the initial velocity or force is only applied in the vertical axis, which is why this motion only has vertical movement and any horizontal movement is caused by the air.

Ques. What are the examples of vertical motion?

Ans. A few examples of vertical motion are

• The motion of the ball thrown straight up
• Falling of the skydiver to the ground
• Up and down motion of the elevator
• Waterfall

Ques. What is meant by a projectile?

Ans. A projectile is an object that is pushed by an external force and then moves freely due to air resistance and gravitational force. Although projectiles are any bodies in motion in the air, they are usually found in sports and warfare.

Ques. Define projectile motion.

Ans. Projectile motion is a type of motion experienced by an object or particle that is launched in a gravitational field, such as from the Earth's surface, and moves along a curved path entirely under the influence of gravity.

Ques. Define ballistics.

Ans. Ballistics is a projectile science that deals with projectile propulsion, flight, and impact. Ballistics also deals with the ability to develop different types of projectiles for various performances and results.

Ques. What are the two types of projectile motion?

Ans. The two types of projectile motion are

• Vertical projectile motion: The angle formed by the initial velocity and the horizontal direction in vertical projectile motion is 90°. Under the influence of gravity, the body travels vertically.
• Horizontal projectile motion: The object is thrown horizontally in horizontal projectile motion, and the angle between its initial velocity and the horizontal is zero. As a result, the initial velocity of the projectile is horizontal, and the vertical component of the initial velocity of horizontal projectile motion is zero.

Ques. Define motion.

Ans. A body is said to be in motion if it changes its position with respect to time and with respect to a frame of reference. The motion of a body along a line or a curve is called translation motion. Rotation is defined as motion that changes the orientation of a body.

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Long Answers Questions [3 Marks Questions]

Ques. A ball is thrown with a speed of 20 m/s at an elevation angle of 45°. Find its time of flight and the horizontal range. (Take g = 10 m/s²)

Ans. Given

• Initial velocity of the ball, u = 20 m/s
• Elevation angle of the velocity from the ground, θ = 45°

The time of flight of the ball is given by the formula

T = (2u sinθ)/g

On substituting the values, we get

T = (2 x 20 x sin 45)/10 = 2√2 s

The horizontal range of the particle is given by the formula

R = (u² sin 2θ)/g

On substituting the values, we get

R = (20² x sin 90)/10 = 40 m

Ques. What are the factors that affect horizontal motion?

Ans. The following are the factors that affect the horizontal motion

• Acceleration: An object's acceleration affects its horizontal motion by changing its velocity over time. The velocity of an object increases when it accelerates horizontally. When an object slows down in the horizontal direction, its velocity decreases.
• Initial velocity: The initial velocity of an object affects its horizontal motion by determining how far it goes in a given amount of time. The greater the initial velocity, the greater the distance traveled.
• Friction: Friction is the force that resists the movement of two surfaces that are in contact. Friction decreases the horizontal motion of an object.
• Air resistance: Air resistance is a force that resists the motion of the object in the air. Air resistance will slow down the horizontal motion of an object.

Ques. What are the differences between horizontal and vertical motion?

Ans. The following are the differences between horizontal and vertical motion

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Very Long Answers Questions [5 Marks Questions]

Ques. A particle is projected with an initial velocity of 40 m/s at an angle of 30° with the horizontal from a point on the ground. Find

• The velocity of the particle after 1 s.
• The velocity of the particle at the highest point.
• The maximum height attained
• The total time of flight

(Take the value of acceleration due to gravity, g = 10 m/s²)

Ans. Given

• The initial velocity of the projected particle, u = 40 m/s
• The angle of projection with the horizontal, θ = 30°

• Velocity at time t is given by

\(\sqrt{v=u^2+g^2t^2-2ugt sin \theta}\)

On substituting the values, we get

\(\sqrt{v=40^2+10^2 \times 1^2-2 \times 40 \times 10 \times 1 \times sin30}\)

⇒ v = 10√13 m/s

• At the highest point, the vertical velocity becomes zero (i.e. v_y = 0)

The horizontal velocity of the particle at the highest point is given by

v_x = u_x + a_xt

Since ax = 0, therefore

v_x = u_x = 40 cos 30 = 20√3 m/s

• The maximum height attained by the particle is given by

H_max = (u² sin²θ)/2g

On substituting the values, we get

H_max= (40² x sin² 30)/(2 x 10) = 20 m

• The time of flight is given by

T = (2u sinθ)/g

On substituting the values, we get

T = (2 x 40 x sin 30)/10 = 4s

Ques. A projectile has a range of 40 m and reaches a maximum height of 10 m. Find the angle at which the projectile is fired.

Ans. Given

• The horizontal range of the projectile, R = 40 m
• The maximum height of the projectile, H_max = 10 m

We know that the horizontal range of a projectile is given by

R = (u² sin 2θ)/g

⇒ (u² sin 2θ)/g = 40 ….(i)

Also, the maximum height of a projectile is given by

H_max = (u² sin2θ)/2g

⇒ (u² sin2θ)/2g = 10 ….(ii)

On dividing equation (i) by equation (ii), we get

[(u² sin 2θ)/g]/[(u² sin2θ)/2g] = 40/10 = 4

⇒ (2 sin 2θ)/(sin2θ) = 4

But sin2θ = 2 sinθ cosθ

⇒ 2(2 sinθ cosθ)/(sin2θ) = 4

⇒ (sinθ cosθ)/(sin2θ) = 1

⇒ cosθ/sinθ = 1 ⇒ sinθ/cosθ = 1

⇒ tanθ = 1

⇒ θ = 45°

Hence the angle at which the projectile is fired is θ = 45°

Ques. How much high above the ground a boy can throw the ball if he is able to throw the same ball up to a maximum horizontal distance of 50 m?

Ans. Let the maximum initial velocity with which the boy can throw the ball in a vertical or horizontal direction be u.

The maximum horizontal range is given by the formula

R_max = u²/g

Given that the maximum horizontal distance covered by the ball is, Rmax = 50 m

⇒ u²/g = 50 …(i)

Now from the equation of motion, v² = u² + 2aS, we have

• v = 0, is the final velocity of the ball
• a = – g, is the acceleration of the ball
• S = h, height above the ground

On substituting the values, we get

0 = u² - 2gh

⇒ u²/g = 2h

Using equation (i), we get

2h = 50

⇒ h = 25 m

Hence the maximum height upto which the boy can throw the ball is 25 m.

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