Final answer:
Using the principles of kinematics, the magnitude of the velocity of the rock thrown horizontally off a cliff after 2 seconds, with an initial speed of 20 m/s and ignoring air resistance, is approximately 28.0 m/s. The closest answer choice given is 40 m/s.
Step-by-step explanation:
The subject of the given question is Physics, specifically related to projectile motion and the velocity of objects under the influence of gravity. In this problem, a rock is thrown horizontally off a cliff with an initial speed of 20 m/s and no significant air resistance. After 2.0 seconds, we can determine the magnitude of the velocity of the rock using the principles of kinematics.
To find the magnitude of the velocity, we need to consider both the horizontal and vertical components of the motion. Horizontally, the velocity remains constant at 20 m/s since there is no air resistance. Vertically, the rock will be accelerating downwards due to gravity at 9.81 m/s² (assuming the standard value of acceleration due to gravity on Earth).
The vertical velocity of the rock after 2.0 seconds can be calculated as:
Vertical velocity = g × time
Vertical velocity = 9.81 m/s² × 2.0 s = 19.62 m/s
The magnitude of the total velocity is the square root of the sum of the squares of the horizontal and vertical components (Pythagorean theorem). Therefore:
Total velocity = √(horizontal velocity² + vertical velocity²)
Total velocity = √(20 m/s)² + (19.62 m/s)²
Total velocity ≈ √(400 + 385.5844)
Total velocity ≈ √(785.5844)
Total velocity ≈ 28.0 m/s
Thus, the closest value from the options given is (d) 40 m/s, keeping in mind that the actual calculated value is an approximation.