An arrow is launched vertically upward from a crossbow at 98.2 m/s. Ignoring air friction, what is its instantaneous acceleration 4.20 s into the flight?
The acceleration will be -g, which is -9.8 m/s^2, at all times. It is directed downward.
It makes no difference what the initial speed or the elapsed time is. Those numbers are put there to confuse you.
Thank you!
23.3
To determine the instantaneous acceleration of the arrow 4.20 seconds into the flight, we first need to understand the concept of acceleration.
Acceleration is defined as the rate of change of velocity. In other words, it measures how quickly an object's velocity is changing at any given moment. Mathematically, acceleration can be calculated using the following formula:
acceleration = (final velocity - initial velocity) / time
Given that the arrow is launched vertically upward, we know that its initial velocity is 98.2 m/s (upward). However, we don't have the final velocity at the 4.20 second mark.
To find the final velocity, we need to consider that the arrow is being launched vertically upward against the force of gravity. Since gravity is constantly acting downward, it will slow the arrow down as it rises until it reaches its peak height and starts coming back down.
At the peak height, the arrow momentarily comes to a stop before starting to descend. Therefore, we can say that the final velocity of the arrow at the 4.20 second mark is 0 m/s.
Now, we have all the necessary values to calculate the instantaneous acceleration:
acceleration = (final velocity - initial velocity) / time
acceleration = (0 m/s - 98.2 m/s) / 4.20 s
Evaluating this equation yields:
acceleration = (-98.2 m/s) / 4.20 s
acceleration ≈ -23.38 m/s²
Therefore, the instantaneous acceleration of the arrow 4.20 seconds into the flight is approximately -23.38 m/s² (downward).