if a block of wood drooped from a tall building has attained a velocity of 78.4 m/s, how long has it been falling?
Assuming no air resistance, falling objects accelerate at the rate of 9.8 m/s/s.
If the object has attained a velocity of 78.4 m/s, it would have fallen 78.4/9.8 = 8 seconds.
To determine how long the block of wood has been falling, we can use the equation of motion for free-falling objects. The equation is given as follows:
v = u + gt
where:
v is the final velocity (78.4 m/s),
u is the initial velocity (0 m/s for a falling object),
g is the acceleration due to gravity (-9.8 m/s^2),
and t is the time.
To find the time, we rearrange the equation:
t = (v - u) / g
Substituting the known values:
t = (78.4 m/s - 0 m/s) / (-9.8 m/s^2)
Simplifying the equation:
t = -7.998 s
Since time cannot be negative, we disregard the negative sign. Therefore, the block of wood has been falling for approximately 8 seconds.
To calculate the time it takes for an object to fall, we can use the kinematic equation for displacement:
s = ut + (1/2) * gt^2,
where s is the displacement, u is the initial velocity, t is the time, g is the acceleration due to gravity (which is approximately 9.8 m/s^2).
In this case, the initial velocity (u) is 0 m/s because the block starts from rest, and the displacement (s) is unknown. However, we know that when the block reaches the ground, its velocity is 78.4 m/s.
To find the displacement, we can use another kinematic equation:
v^2 = u^2 + 2g * s,
where v is the final velocity.
Plugging in the values:
78.4^2 = 0 + 2 * 9.8 * s,
6159.36 = 19.6s,
s = 6159.36 / 19.6 = 314.88 m.
Now that we have the displacement, we can calculate the time using the first equation:
314.88 = 0 * t + (1/2) * 9.8 * t^2,
314.88 = 4.9t^2,
t^2 = 314.88 / 4.9,
t^2 = 64,
t = √64,
t = 8 seconds.
Therefore, the block has been falling for 8 seconds.