A 2.15 kg book is dropped from a height of
1.8 m.
a) What is its acceleration?
Answer in units of m/s2.
anything falling has the acceleration due to gravity, 9.8m/s^2
i tried that i don't know why its not right
i put -9.8m/s^2
it worked:)
To calculate the acceleration, we can use the equation of motion:
π = π’π‘ + 0.5ππ‘^2
Where:
π = distance (in this case, the height) = 1.8 m
π’ = initial velocity = 0 m/s (as the book is dropped)
π‘ = time taken to fall
π = acceleration (what we need to find)
Since the book is only falling vertically under the force of gravity, we can use the equation for gravitational acceleration:
π = π β 9.8 m/s^2
Substitute the given values into the equation of motion:
1.8 = 0.5 * 9.8 * π‘^2
To solve for π‘^2, we can rearrange the equation:
0.5 * 9.8 * π‘^2 = 1.8
Multiply both sides by 2:
9.8 * π‘^2 = 3.6
Divide both sides by 9.8:
π‘^2 = 3.6 / 9.8
Take the square root of both sides to solve for π‘:
π‘ = β(3.6 / 9.8)
π‘ β 0.6709 s
Now that we have the time, we can substitute it back into the equation of motion to find the acceleration:
π = (π - π’π‘) / (0.5π‘^2)
π = (1.8 - 0) / (0.5 * 0.6709^2)
π β 5.42 m/s^2
So, the acceleration of the book is approximately 5.42 m/s^2.