Question

Section A (MCO) & VSA 1 MARKS Questi 1 Select and write the correct answer: (i) Trajectory of any motion is decided by (a) acceleration (b) initial velocity (c) both a and b (d) None of these ​

Answer 1

thrown (projected) into the air. After the initial force that launches the object, it only experiences the force of gravity. The object is called a projectile, and its path is called its trajectory. As an object travels through the air, it encounters a frictional force that slows its motion called air resistance. Air resistance does significantly alter trajectory motion, but due to the difficulty in calculation, it is ignored in introductory physics.

The most important concept in projectile motion is that horizontal and vertical motions are independent, meaning that they don’t influence one another. Figure 5.27 compares a cannonball in free fall (in blue) to a cannonball launched horizontally in projectile motion (in red). You can see that the cannonball in free fall falls at the same rate as the cannonball in projectile motion. Keep in mind that if the cannon launched the ball with any vertical component to the velocity, the vertical displacements would not line up perfectly.

Since vertical and horizontal motions are independent, we can analyze them separately, along perpendicular axes. To do this, we separate projectile motion into the two components of its motion, one along the horizontal axis and the other along the vertical.

A cannonball is sitting on a flat surface. Dotted lines show the projectile motion of a cannon ball. Dotted line A shows the ball dropping vertically. Dotted line B shows a curved path. Dotted line C shows the ball moving horizontally.

Figure 5.27 The diagram shows the projectile motion of a cannonball shot at a horizontal angle versus one dropped with no horizontal velocity. Note that both cannonballs have the same vertical position over time.

We’ll call the horizontal axis the x-axis and the vertical axis the y-axis. For notation, d is the total displacement, and x and y are its components along the horizontal and vertical axes. The magnitudes of these vectors are x and y, as illustrated in Figure 5.28.

A boy is kicking a soccer ball. A curved line shows the ball's motion. A right triangle is drawn with vectors using an x-y axis. The hypotenuse is labeled d, the vertical leg is labeled y and the horizontal leg is labeled x.

Answer 2

The trajectory of any motion is decided by both acceleration and initial velocity

• (c) both a and b is the correct option.
• Acceleration determines how quickly an object's velocity changes over time, while initial velocity determines the starting point and direction of motion. Both of these factors are crucial in determining the path that an object takes during motion.
• Acceleration is the rate of change of velocity over time and can influence the trajectory of an object by changing the direction and speed of the movement. Initial velocity, on the other hand, dictates the initial direction and speed of the object before it is affected by any acceleration.
• Acceleration is responsible for how fast the motion is changing its direction and velocity is responsible for the starting direction.

Hence, the correct answer is (c) both a and b.

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