a rubber ball is thrown downwards off a balcony. after it travels 55m it has a speed of 46.5m/s. what is the initial velocity
V^2 = Vo^2 + 2g*d = 46.5^2
Vo^2 + 19.6*55 = 2162
Vo^2 = 2162 - 1078 = 1084
Vo = 32.92 m/s.
To find the initial velocity of the rubber ball, we can use the equation that relates final velocity, initial velocity, acceleration, and displacement:
vf^2 = vi^2 + 2ad
Where:
vf = final velocity
vi = initial velocity
a = acceleration
d = displacement
In this case, the ball is thrown downwards, so we can assume the acceleration due to gravity (g) is acting in the same direction as the motion. The value of acceleration due to gravity varies depending on the location, but for simplicity, we can assume it is approximately 9.8 m/s^2.
Given:
vf = 46.5 m/s
d = -55 m (negative because it is in the downward direction)
a = -9.8 m/s^2 (also negative as it acts in the downward direction)
Now we can substitute the given values into the equation and solve for the initial velocity (vi):
vf^2 = vi^2 + 2ad
46.5^2 = vi^2 + 2 * (-9.8) * (-55)
2162.25 = vi^2 + 1078
Rearranging the equation to solve for vi:
vi^2 = 2162.25 - 1078
vi^2 = 1084.25
Finally, we take the square root of both sides to find the initial velocity:
vi ≈ √1084.25
vi ≈ 32.92 m/s (approximately)
Therefore, the initial velocity of the rubber ball when it was thrown downwards off the balcony is approximately 32.92 m/s.