A child drops a coin from the window of a house.it strikes the ground 0,8 s later.what is the magnitude and direction of the coin's acceleration?
To determine the magnitude and direction of the coin's acceleration, we need to first find the coin's initial velocity and the distance it fell.
From the given information, we know:
- The time it took the coin to strike the ground, which is 0.8 seconds.
- The acceleration due to gravity, which is typically denoted as -9.8 m/s^2 (assuming downward direction).
To find the initial velocity, we can use the equation of motion:
v = u + at
Where:
- v is the final velocity (which is 0 m/s when the coin reaches the ground).
- u is the initial velocity (what we want to find).
- a is the acceleration due to gravity (-9.8 m/s^2).
- t is the time taken (0.8 s).
Rearranging the equation, we have:
u = v - at
Substituting the values, we get:
u = 0 - (-9.8 * 0.8)
u = 0 + 7.84
u ≈ 7.84 m/s
The initial velocity of the coin is approximately 7.84 m/s.
Next, we can find the distance the coin fell using the equation of motion:
s = ut + 0.5at^2
Where:
- s is the distance (what we want to find).
- u is the initial velocity (7.84 m/s).
- a is the acceleration due to gravity (-9.8 m/s^2).
- t is the time taken (0.8 s).
Substituting the values, we have:
s = (7.84 * 0.8) + 0.5 * (-9.8) * (0.8^2)
s = 6.272 - 3.136
s ≈ 3.14 m
The distance the coin fell is approximately 3.14 meters.
Now, we can determine the magnitude and direction of the coin's acceleration. Since the coin is falling downward, its acceleration is directed downward with a magnitude equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.