Question

An airplane flying with a horizontal initial velocity of 80 m/s drops a package down to the ground. The plane is initially 490 meters above the ground.

a) How long does it take the package to hit the ground?

a) 6.125 s
b) 7.5 s
c) 10 s
d) 12.25 s

Answer 1

The time it takes for a package to hit the ground when dropped from a height of 490 meters, assuming no air resistance and no initial vertical velocity, is approximately 10 seconds. This is calculated using the kinematic equation for objects in free fall.

Step-by-step explanation:

To determine how long it takes for a package to hit the ground when dropped from an airplane with an initial horizontal velocity, we can use the kinematic equations for objects in free fall, assuming no air resistance. The time of fall depends only on the initial height and the acceleration due to gravity, which is approximately 9.81 m/s2 on Earth. The initial horizontal velocity of the plane does not affect the time it takes for the package to drop, only the horizontal distance it will travel before impact.

Calculating the Time of Fall

Using the equation s = ut + 0.5at2, where 's' is the vertical distance, 'u' is the initial vertical velocity (which is 0 in this case), 'a' is the acceleration due to gravity, and 't' is time, we can solve for 't' when s is 490 meters.

s = 0.5 * g * t2

By rearranging the equation to solve for 't', we get t = sqrt(2s/g). Plugging in the values s = 490 m and g = 9.81 m/s2, we can calculate the time it takes for the package to reach the ground.

Using the above equation, the calculation for 't' yields approximately 10 seconds, which matches one of the options given by the student, specifically option (c) 10 s.