Magnitude of the overall Velocity problem

[jbutl3r25]

1. A plane drops a package from a height of 3230 m. The plane's horizontal velocity was 110 m/s at the instant the package was dropped. What is the magnitude of the overall velocity of the hamper at the instant it touches the ground?



2. d=vo(t) + 1/2at^2



3. dx
vx 110
t 25.7

vfY
voY 0
aY -9.8
dY -3230
t 25.7

I found the time from the equation above. How would you find the overall velocity, and then how would you find the magnitude of the overall velocity?

 

[dontdisturbmycircles]

Calculate the final velocity by using the fact that the box is experiencing a constant acceleration. To find the 'overall' velocity, note velocity's vector nature.

 

[m2003]

The overall velocity of the hamper can be found by combining the horizontal and vertical components of its velocity. The horizontal velocity remains constant at 110 m/s, while the vertical velocity changes due to the acceleration of gravity. This can be calculated using the equation vfY = voY + aYt, where vfY is the final vertical velocity, voY is the initial vertical velocity (in this case, 0), aY is the acceleration due to gravity (-9.8 m/s^2), and t is the time calculated in part 3.

To find the overall velocity, we can use the Pythagorean theorem, which states that the magnitude of the overall velocity is equal to the square root of the sum of the squares of the horizontal and vertical velocities. In this case, the magnitude of the overall velocity would be the square root of (110^2 + vfY^2).

To find the numerical value of the magnitude of the overall velocity, we can plug in the values calculated in part 3 and the final vertical velocity calculated in the previous step into the equation above. This will give us the numerical value of the overall velocity at the instant the hamper touches the ground.