Projectile Motion airplane final speed

[black_hole]

Homework Statement

An airplane flying 914 m above the ocean at 116 km/hr is supposed to drop a box of emergency supplies to the survivors of a shipwreck on an island. At what final speed will the supplies land on the island?

Homework Equations

The Attempt at a Solution

So Vx = 32.222 m/s, is Voy = 0 m/s?
a = -9.8 m/s/s and y = -914 m?

So I did Vfy^2 = Voy^2 +2ay and got -133.845 m/s, but that is not right...

 

[Doc Al]

So I did Vfy^2 = Voy^2 +2ay and got -133.845 m/s, but that is not right...

That's just the y-component of the velocity. Combine it with the x-component to figure out the speed.

 

[kerimek]

Your initial attempt at a solution is on the right track, but there are a few errors in your calculations. Let's break down the problem and equations step by step to find the correct answer.

First, let's define our variables. Vx is the horizontal velocity of the airplane, which is given as 116 km/hr. We need to convert this to m/s, so Vx = 116 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 32.222 m/s. This part of your calculation is correct.

Next, we need to find the vertical velocity of the airplane, Voy. Since the airplane is flying at a constant altitude, we can assume that Voy = 0 m/s. This is because there is no change in altitude, so there is no vertical acceleration.

Now, we can use the equation Vfy^2 = Voy^2 + 2ay to find the final vertical velocity of the supplies, Vfy. We know that Vfy = 0 m/s, Voy = 0 m/s, and y = -914 m. Plugging these values in, we get 0 = 0 + 2(-9.8 m/s^2)(-914 m). Solving for Vfy, we get Vfy = 42.6 m/s.

Finally, we need to find the final speed of the supplies when they land on the island. This will be the resultant velocity, which is found using the Pythagorean theorem: Vfinal = √(Vx^2 + Vfy^2) = √(32.222 m/s)^2 + (42.6 m/s)^2) = 53.5 m/s.

Therefore, the final speed of the supplies when they land on the island is 53.5 m/s. This calculation takes into account the horizontal and vertical components of the velocity, and is the correct answer for this problem.