A rock dropped from a small bridge encounters no air resistance and hits the pond below 1.0 s later.
If it had been thrown horizontally with a speed of 10 m/s, then it would have hit the water
A. more than 1.0 {s} later, since it has a greater distance to travel.
B. 1.0 {s} later, since the vertical motion is not affected by the horizontal motion.
C. less than 1.0 {s} later, since the higher speed would tend to get the ball to the ground more quickly.
Answer:
B. 1.0s later, since the vertical motion is not affected by the horizontal motion
1) A simple harmonic motion is described by a = - 16x, where a is acceleration in m/s2 and x is displacement in m. What is the time period?
To answer this question, we need to understand the motion of a horizontally thrown object and a vertically dropped object.
Let's consider the rock dropped vertically first. When an object is dropped vertically, it falls due to the force of gravity. The only force acting on it is the downward force of gravity, so it undergoes free fall. Ignoring air resistance, its vertical motion is not affected by any horizontal motion. Therefore, the time taken for it to hit the water is determined solely by its vertical motion. This means that dropping a rock from the small bridge and hitting the pond will take 1.0 second, as given in the question.
Now let's consider the rock thrown horizontally with a speed of 10 m/s. When an object is thrown horizontally, it still experiences the force of gravity in the downward direction. However, it also has an initial horizontal velocity. As there is no vertical force acting in the horizontal direction, the horizontal velocity remains constant throughout the motion. Meanwhile, the rock will still fall vertically due to gravity.
Since the vertical and horizontal motions are independent of each other, the time taken for the horizontally thrown rock to hit the water will be the same as the time taken for the vertically dropped rock to hit the water. Therefore, the answer is B: 1.0 second later because the vertical motion is not affected by the horizontal motion.
To summarize, both the vertically dropped rock and the horizontally thrown rock will hit the water at the same time, regardless of the horizontal velocity of the thrown rock.