Select the motion diagram that corresponds to each of the four situations. E.g., if diag. A corresponds to the first situation, diag. C to the second, and none of the diagrams to situations 3 and 4, enter ACNN. Note that the velocity and acceleration vectors are shown; both must be correct!
(i) A ball is thrown horizontally off a high cliff.
(ii) Joe is driving his car at a steady speed, then `puts the pedal to the metal' and accelerates.
(iii) Galileo drops a ball from the Leaning Tower of Pisa. Consider its motion from when it leaves his hand until a moment before it hits the ground.
(iv) A ball rolls down a smooth board tilted at a 15° angle.
To determine the motion diagram that corresponds to each of the four situations, we need to consider the characteristics of the motion involved.
(i) A ball thrown horizontally off a high cliff:
In this situation, the velocity of the ball is purely horizontal due to the horizontal throw. However, the acceleration acting on the ball is in the vertical direction due to the force of gravity. Therefore, the motion diagram that corresponds to this situation would have a horizontal velocity vector and a vertical downward acceleration vector.
(ii) Joe driving his car at a steady speed, then accelerating:
When Joe is driving his car at a steady speed, the velocity of the car remains constant in both magnitude and direction. Therefore, the motion diagram would have a constant velocity vector. When Joe accelerates by "putting the pedal to the metal," the velocity of the car increases in magnitude. Hence, the motion diagram for this situation would show an increasing magnitude of the velocity vector. However, since the direction of the car's velocity remains unchanged, the acceleration vector in the motion diagram would be zero.
(iii) Galileo dropping a ball from the Leaning Tower of Pisa:
When Galileo drops a ball from the Leaning Tower of Pisa, the initial velocity of the ball is zero as it is at rest. However, gravity causes the ball to accelerate downward with a constant magnitude. Therefore, the motion diagram for this situation would have a velocity vector pointing downwards (representing the acceleration due to gravity) while the acceleration vector would also point downwards.
(iv) A ball rolling down a smooth board tilted at a 15° angle:
When a ball rolls down a smooth board tilted at an angle, its velocity vector will be inclined in the direction of the downward slope. The magnitude of the velocity vector will increase as the ball accelerates downwards under the influence of gravity and the slope of the board. Therefore, the motion diagram for this situation would have a velocity vector pointing downwards at an angle of 15° (matching the tilt of the board) and an acceleration vector pointing straight downwards.
Based on these explanations, the corresponding motion diagrams for each situation would be:
(i) A ball thrown horizontally off a high cliff: A
(ii) Joe driving his car at a steady speed, then accelerating: C
(iii) Galileo dropping a ball from the Leaning Tower of Pisa: D
(iv) A ball rolling down a smooth board tilted at a 15° angle: A