You stand on top a building 44 m tall with a water balloon. You drop the water balloon from rest. How fast is the balloon moving when it is halfway down the building? (assume no friction)
A.20.78 m/s
B.39.81 m/s
C.19.68 m/s
D.26.92 m/s
22 = (9.8/2)t^2
so
t= sqrt(44/9.8)
v = 9.8 t
im confused.... is it C?
well, is 9.8*sqrt(44/9.8) = 19.68?
V^2 = Vo^2 + 2g*d = 0 + 19.6*22 = 431.2.
V =
To find the speed at which the water balloon is moving when it is halfway down the building, we can use the laws of motion and the principles of conservation of energy.
First, we need to determine the distance that the balloon needs to travel to reach the halfway point of the building. Since the building is 44 m tall, the halfway point is at a height of 44/2 = 22 m.
Using the equation for motion under gravity, we can determine the time it takes for the balloon to fall from rest to the halfway point. The equation is:
s = ut + (1/2)gt^2
Where:
s = distance (22 m)
u = initial velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time
Plugging in the values, the equation becomes:
22 = 0*t + (1/2)(-9.8)t^2
Simplifying the equation gives:
-4.9t^2 + 22 = 0
Now, we can solve this quadratic equation for t by factoring or using the quadratic formula. Factoring the equation gives:
(-2t + 7)(2t - 7) = 0
Setting each factor equal to 0 gives two possible values for t:
-2t + 7 = 0 or 2t - 7 = 0
Solving each equation gives:
-2t = -7 or 2t = 7
t = 7/2 or t = 7/2
Since time cannot be negative, we take t = 7/2 = 3.5 seconds as the time it takes for the balloon to reach the halfway point of the building.
Now, we can find the speed of the balloon at this point by using the equation for velocity:
v = u + gt
Plugging in the values, the equation becomes:
v = 0 + (-9.8)(3.5)
v = -34.3 m/s
The negative sign indicates that the velocity is directed downward. However, we need the magnitude of the velocity, so we take the absolute value:
v = 34.3 m/s
Therefore, the speed of the balloon when it is halfway down the building is 34.3 m/s.
None of the given options is a perfect match, but the closest one is D. 26.92 m/s.