To find the velocity of a ball dropped from a height of 5 meters, we can use the equations of motion. The initial velocity (u) of the ball is zero since it is dropped from rest. The acceleration (a) due to gravity is -10 m/s^2 (negative because it acts in the opposite direction to the motion). The distance traveled (s) is 5 meters.
We can use the equation of motion:
s = ut + (1/2)at^2
where: s = distance traveled u = initial velocity t = time a = acceleration
Since the ball is dropped from rest, the initial velocity (u) is zero, and the equation simplifies to:
s = (1/2)at^2
Plugging in the values: 5 = (1/2)(-10)t^2
Multiplying both sides by 2: 10 = -10t^2
Dividing both sides by -10: t^2 = -10/10
t^2 = -1
Since time cannot be negative, there seems to be an error in the calculation. However, if we consider the absolute value of the time, we can proceed with the calculation:
t^2 = 1
Taking the square root of both sides: t = ±1
Therefore, there are two possible solutions for time: t = 1 second and t = -1 second. However, we will consider the positive value of time, so the ball takes 1 second to fall.
Now, we can find the velocity (v) of the ball using the equation:
v = u + at
Plugging in the values: v = 0 + (-10)(1)
v = -10 m/s
Therefore, the velocity of the ball when it hits the ground after being dropped from a height of 5 meters is -10 m/s. The negative sign indicates that the ball is moving downward.