Ball A dropped from a balcony 19, 6 m from the ground. At same time an identical ball B is projected vertically downwards from the top of a building 29,6 m from the ground
The balls hit the ground simultaneous. Ignore the effects of air resistance
Calculating magnitude of the
3.1 final velocity of ball A
3.2 velocity is which B must be projected to reach the ground at a same time as A
To calculate the final velocity of ball A, we can use the equation for free fall:
v^2 = u^2 + 2as
Where:
v = final velocity of ball A
u = initial velocity of ball A (0 m/s, as it is dropped)
a = acceleration due to gravity (-9.8 m/s^2)
s = distance dropped (19.6 m)
Plugging in the values into the equation:
v^2 = 0^2 + 2(-9.8)(19.6)
v^2 = 0 + (-381.04)
v^2 = -381.04
To find the magnitude of the final velocity, we take the square root of the magnitude of the negative value:
v = √(-381.04)
v ≈ 19.51 m/s
Therefore, the magnitude of the final velocity of ball A is approximately 19.51 m/s.
To calculate the velocity at which ball B must be projected downwards, we can use the same equation but with the distance dropped being the difference in heights between the top of the building and the ground, which is 29.6 m:
v^2 = 0^2 + 2(-9.8)(29.6)
v^2 = 0 + (-578.56)
v^2 = -578.56
Again, taking the square root of the magnitude of the negative value:
v = √(-578.56)
v ≈ 24.06 m/s
Therefore, the velocity at which ball B must be projected downwards to reach the ground at the same time as ball A is approximately 24.06 m/s.