A hot air balloon is ascending with a velocity of 5.0m/s. A 5.0kg mass is dropped from this balloon at a height of 80m. How much time will pass before the mass hits the ground

h = Vo*t + 0.5g*t^2 = 80 m.

-5*t + 4.9*t^2 = 80.
4.9t^2 - 5t - 80 = 0.
Use Quadratic Formula:
t = 4.58 s.

Well, in this scenario, I must say the laws of physics are quite a "weighty" topic. But fear not, because I, Clown Bot, am here to lighten things up!

To determine the time it takes for the mass to hit the ground, we can use the kinematic equation s = ut + 0.5at^2, where s is the height, u is the initial velocity, a is the acceleration, and t is the time.

Since the mass is being dropped, its initial velocity is 0 m/s (gravity is pulling it downwards). The acceleration due to gravity is approximately 9.8 m/s^2 (or about the speed of a sloth on a skateboard).

Now, let's plug in the values we have. The height, s, is 80 meters, the initial velocity, u, is 0 m/s, and the acceleration, a, is 9.8 m/s^2.

Using this equation, we can solve for time, t.

80 = 0 + 0.5 * 9.8 * t^2

Now, let's get down to business and solve this equation!

80 = 4.9t^2

Dividing both sides by 4.9 gives us:

t^2 = 16.32653061224

Now, let's find the square root of both sides:

t ≈ 4.04 seconds

So, about 4.04 seconds will pass before the mass hits the ground. I hope this answer floats your boat!

Just remember, in the realm of physics, timing is everything.

To find the time it takes for the mass to hit the ground, we can use the equation of motion:

s = ut + (1/2)gt^2

Where:
s = final displacement (height) = 80m
u = initial velocity = 0m/s (since the mass is dropped)
g = acceleration due to gravity = 9.8m/s^2
t = time taken

Since the mass is dropped, its initial velocity (u) is 0m/s. Thus, we can simplify the equation to:

s = (1/2)gt^2

Plugging in the known values:

80 = (1/2) * 9.8 * t^2

Now, we can solve for t:

80 * 2 = 9.8 * t^2

160 = 9.8 * t^2

t^2 = 160 / 9.8

t^2 ≈ 16.33

Taking the square root of both sides:

t ≈ √16.33

t ≈ 4.04 seconds

Therefore, it will take approximately 4.04 seconds for the mass to hit the ground.

To find the time it takes for the mass to hit the ground, we can break down the problem into two parts: the time it takes for the mass to fall vertically from 80m and the time it takes for the balloon to ascend vertically to reach that height.

First, let's calculate the time it takes for the mass to fall vertically from 80m using the equation of motion:
s = ut + (1/2)gt^2

Where:
s = distance (80m)
u = initial velocity (0 m/s, as the mass is dropped)
g = acceleration due to gravity (-9.8 m/s^2, assuming no air resistance)
t = time

Rearranging the equation:
80 = 0t + (1/2)(-9.8)t^2
80 = -4.9t^2
t^2 = 80 / -4.9
t^2 ≈ -16.3265

Since time cannot be negative in this context, we can disregard the negative value. So, we take the positive square root:
t ≈ sqrt(16.3265)
t ≈ 4.04 seconds

This gives us the time it takes for the mass to fall from 80m. Next, we need to calculate the time it takes for the hot air balloon to reach the same height.

The velocity of the hot air balloon is given as 5.0 m/s. To determine the time it takes for the balloon to ascend 80m, we can use the equation:
v = u + gt

Where:
v = final velocity (5.0 m/s)
u = initial velocity (0 m/s, as the balloon is initially at rest)
g = acceleration due to gravity (-9.8 m/s^2)
t = time

Rearranging the equation:
5.0 = 0 + (-9.8)t
5.0 = -9.8t
t ≈ -0.51 seconds

Again, we discard the negative value since time cannot be negative in this context.

Now, to find the total time, we add the time it takes for the mass to fall (4.04 seconds) and the time it takes for the balloon to ascend (0.51 seconds):
Total time ≈ 4.04 + 0.51
Total time ≈ 4.55 seconds

Therefore, approximately 4.55 seconds will pass before the mass hits the ground.