How Fast Does a Package Travel When Dropped from a Plane?

[1man]

A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 260 mph at an altitude of 750 m. The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80 m/s^2.

What is the speed v_f of the package when it hits the ground?
Express your answer numerically in miles per hour.

i know the problem requires sqrt((v_0-v_1)²+(g*sqrt(2h/g))²)

i got 2395.6 but i want someone to check my answer for me thank you in advance

 

[anathema]

Hello there,

I'm not sure where you got the formula you mentioned, as it seems to be missing some variables and doesn't match the given information in the problem. The correct formula to use in this situation is the kinematic equation: v_f = v_0 + at, where v_f is the final velocity, v_0 is the initial velocity, a is the acceleration, and t is the time.

In this case, we can assume that the initial velocity (v_0) of the package is the same as the horizontal speed of the airplane, which is 260 mph. The acceleration (a) is the acceleration due to gravity, which is given as 9.80 m/s^2. To solve for the final velocity (v_f), we need to find the time (t) it takes for the package to fall from the release point to the ground.

To find the time, we can use the kinematic equation: h = v_0t + (1/2)at^2, where h is the height (750 m) and v_0 is the initial velocity (260 mph). Solving for t, we get t = 8.37 seconds.

Now, we can plug in the values we have into the first equation: v_f = v_0 + at. This gives us v_f = 260 mph + (9.80 m/s^2)(8.37 s). Converting the units, we get v_f = 260 mph + 23.84 mph = 283.84 mph.

Therefore, the final speed of the package when it hits the ground is approximately 283.84 mph.

I hope this helps! Let me know if you have any further questions.