A helicopter is ascending up at a rate of 12 m/s. At a height of 80m above a package is dropped. How long does the package take to reach the ground?
To find the time it takes for the package to reach the ground, we can use the formula:
time = distance / velocity
First, let's calculate the time it takes for the package to fall from a height of 80m. We can find this using the equation for free fall:
distance = (1/2) * acceleration * time^2
Since the package is falling due to gravity, we can use an acceleration of 9.8 m/s^2. Plugging in the values, we have:
80 = (1/2) * 9.8 * time^2
Simplifying the equation, we get:
80 = 4.9 * time^2
Divide both sides by 4.9:
16.3265 = time^2
Taking the square root of both sides:
time ≈ 4.04 seconds
So the time it takes for the package to fall from a height of 80m is approximately 4.04 seconds.
Now, let's find the time it takes for the helicopter to ascend 80m at a rate of 12 m/s. We can use the formula:
time = distance / velocity
Plugging in the values, we have:
time = 80 / 12
time ≈ 6.67 seconds
Therefore, the total time it takes for the package to reach the ground is the sum of the time it takes for the package to fall and the time it takes for the helicopter to ascend:
total time ≈ 4.04 + 6.67
total time ≈ 10.71 seconds
So the package takes approximately 10.71 seconds to reach the ground.
just plug into the usual formula and solve for t when h(t)=0.
h(t) = 80 + 12t - 4.9t^2