a student dropped her notebook from her desk. It took 0.5 s to reach the floor. What was the eraser’s speed just before hitting the ground? *
speed in a free-fall in m/s:
v = 9.8t metres/second
when t=2s
v = 9.8(2( m/s)
= ......
To find the eraser's speed just before hitting the ground, we need to know the distance it fell and the time it took to fall.
We can use the equation of motion:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the eraser starts from rest (initial velocity is 0) and we are only considering the vertical motion (acceleration due to gravity), the equation simplifies to:
distance = 0.5 * acceleration * time^2
In this case, we are given the time it took to reach the floor, which is 0.5 seconds. However, we still need to determine the distance the eraser fell.
To find the distance, we use the equation:
distance = 0.5 * gravity * time^2
Assuming the acceleration due to gravity is 9.8 m/s^2 (on Earth), we can substitute the values into the equation:
distance = 0.5 * 9.8 m/s^2 * (0.5 s)^2
distance = 0.5 * 9.8 m/s^2 * 0.25 s^2
distance = 1.225 m
Now we can find the eraser's speed just before hitting the ground by using another equation of motion:
final velocity = initial velocity + (acceleration * time)
Since the eraser starts from rest, the initial velocity is 0 and the equation simplifies to:
final velocity = acceleration * time
Substituting the values into the equation:
final velocity = 9.8 m/s^2 * 0.5 s
final velocity = 4.9 m/s
Therefore, the eraser's speed just before hitting the ground was 4.9 m/s.
To find the eraser's speed just before hitting the ground, we need to use the equation for speed, which is defined as the distance traveled divided by the time taken.
Now, we don't have the distance traveled, but we know that the eraser was dropped from the desk and landed on the floor. Assuming the eraser fell vertically, the distance traveled is the height from the desk to the ground.
Let's say we measure the height in meters. We can use the equation:
distance = 0.5 * g * t^2
Where:
- distance is the height of the desk to the ground
- g is the acceleration due to gravity (9.8 m/s^2)
- t is the time taken for the eraser to reach the ground (0.5 s)
Using the provided information, we can calculate the height:
distance = 0.5 * 9.8 * (0.5)^2
distance = 0.5 * 9.8 * 0.25
distance = 1.225 m (rounded to three decimal places)
Now that we have the distance traveled, we can find the speed just before hitting the ground:
speed = distance / time
speed = 1.225 / 0.5
speed = 2.45 m/s (rounded to two decimal places)
Therefore, the eraser's speed just before hitting the ground was approximately 2.45 m/s.