39.09987212 m/s
There are a couple of ways to solve this problem. We can use the equation for the distance an object moves under a constant acceleration of 9.8 m/s^2, or we can calculate the kinetic energy an object will have after falling 78 meters and from there calculate the velocity. Let's first use the constant acceleration formula:
d = 0.5 AT^2
78 m = 0.5 * 9.8 m/s^2 * T^2
78 m = 4.9 m/s^2 * T^2
15.91836735 s^2 = T^2
3.98978287 = T
So we now know it takes 3.98978287 second for the brick to hit the ground. And at an acceleration of 9.8 m/s^2 we get:
3.98978287 s * 9.8 m/s^2 = 39.09987212 m/s
Now let's try using the energy method. I will assume that the mass of the brick is 1 kg, but any non-zero value will do. So
78 m * 9.8 m/s^2 * 1 kg = 764.4 kg*m^2/s^2
And kinetic energy is expressed as
KE = 0.5 mv^2
So
764.4 kg*m^2/s^2 = 0.5 1 kg * v^2
764.4 kg*m^2/s^2 = 0.5 kg * v^2
1528.8 m^2/s^2 = v^2
39.09987212 m/s = v
So the determine how long it takes and multiply by the acceleration method gives 39.09987212 m/s.
And the use the energy to determine the velocity gives 39.09987212 m/s.
So it doesn't matter which of the two methods you use. But, personally, I think the energy method is simpler, although the time method is more direct.
