You are trying to find out how high you have
to pitch a water balloon in order for it to burst
when it hits the ground. You discover that
the balloon bursts when you have pitched it
to a height of 13 m.
With what velocity did the balloon hit
the ground? The acceleration of gravity is
9.8 m/s
2
. The positive direction is up, so the
velocity when it hits is negative.
Answer in units of m/s. Please Help
Well, let's calculate this in a humorous way!
First, we need to determine the initial velocity of the water balloon when it was pitched.
To do that, we can use the equation: vf^2 = vi^2 + 2ad
But since we know the balloon burst at its highest point, we can assume its final velocity is 0.
So, we have 0 = vi^2 + 2ad
Now, we need to solve for vi, which will give us the initial velocity when the balloon was pitched.
Dividing both sides of the equation by 2ad, we get:
vi^2 = -2ad
Taking the square root of both sides, we now have:
vi = √(-2ad)
Now, let's plug in the given values:
a = 9.8 m/s^2 (acceleration due to gravity)
d = 13 m (height to burst)
So, vi = √(-2 * 9.8 m/s^2 * 13 m)
Calculating this, we find the initial velocity (when the balloon was pitched) to be approximately 18.66 m/s.
But wait, since the velocity when it hits the ground is negative, the answer is -18.66 m/s.
So, the water balloon hit the ground with a velocity of approximately -18.66 m/s.
Just make sure you're not standing under it when it bursts, or you might get a refreshing surprise!
To find the velocity at which the balloon hits the ground, you can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (the velocity when the balloon hits the ground)
u = initial velocity (in this case, the velocity when the balloon was pitched upwards)
a = acceleration (the acceleration due to gravity, which is -9.8 m/s^2 due to it being in the opposite direction)
s = displacement (the height the balloon was pitched, which is 13 m)
Since we are solving for the final velocity (v), we rearrange the equation:
v^2 = u^2 + 2as
v^2 = 0 + 2(-9.8)(13)
v^2 = -254.8
Since the velocity cannot be negative according to the given information, we take the square root of 254.8 to find the absolute value of the velocity:
v = √254.8
v ≈ 15.97
The velocity at which the balloon hits the ground is approximately 15.97 m/s. Since the positive direction is up and the velocity when it hits is negative, the final velocity is -15.97 m/s.
V^2 = Vo^2 + 2g*h = 0 + 19.6*13 = 254.8,
V = 16 m/s.