A helicopter is ascending vertically with a speed of 5.20m/s . At a height of 110m above the Earth, a package is dropped from a window.
How much time does it take for the package to reach the ground? [Hint: for the package equals the speed of the helicopter.]
height = 110 + 5.5 t - 4.9 t^2 = 0
Solve that quadratic equation for t. Take the positive solution.
To find the time it takes for the package to reach the ground, we can use the equation of motion for free-falling objects. The equation is:
d = 1/2 * g * t^2
where:
d is the distance traveled (in this case, 110m),
g is the acceleration due to gravity (approximately 9.8m/s^2), and
t is the time.
Rearranging the equation to solve for time (t), we get:
t = sqrt(2 * d / g)
Substituting the given values into the equation:
t = sqrt(2 * 110m / 9.8m/s^2)
Calculating this expression:
t = sqrt(22.45)
Therefore, the time it takes for the package to reach the ground is approximately 4.74 seconds.