A boy standing on top a building with a height of 500m throws a ball vertically upwards. The balls take 40s to reach to the ground. Neglecting the height of the boy throwing the ball, determine the velocity of the ball.
0 = -.5 g (40^2) + Vo(40) + 500
solve for Vo (the throwing velocity)
Vo / g is the time to max height
40 - (Vo / g) is the free fall time
(40 * g) - Vo is the impact velocity
To determine the velocity of the ball, we need to use the equation of motion for an object in free fall.
The equation is: v = u + at
Where:
v = Final velocity
u = Initial velocity
a = Acceleration
t = Time taken
In this case, the ball is thrown vertically upwards, so the initial velocity (u) will be positive since it is going against the direction of gravity. The final velocity (v) will be zero when the ball reaches its highest point. Therefore, we can rewrite the equation as follows:
0 = u - gt
Where g is the acceleration due to gravity, which is approximately 9.8 m/s².
Now, let's calculate the initial velocity of the ball:
0 = u - (9.8 m/s²)(40 s)
Rearranging the equation:
u = (9.8 m/s²)(40 s)
u = 392 m/s
Therefore, the initial velocity of the ball, when it is thrown vertically upwards, is 392 m/s.