Calculating Time for Falling Crate in Projectile Motion

[bringme2life]

This is my first post here so please bear with me if I'm doing something wrong

Homework Statement

A cargo plane is flying horizontally at an altitude of 10.1 km with a speed of 910 km/h when a large crate falls out of the rear loading ramp. (Ignore any effects due to air resistance.) How long does it take the crate to hit the ground?

I converted everything to meters.

Yf = 0m
Yi = 10100m
Yxi = 252.78 m/s
g = -9.81 m/s

Homework Equations

Xf = Xi + Vxi*t
Yf = Yi + Vyi*t - 4.905(t)^2

The Attempt at a Solution

My problem is figuring out Vyi in this case so that I can plug it into my second equation to solve for time. Can anyone give me a push in the right direction?

 

[rl.bhat]

In the given problem vyi = 0.

 

[tomcue]

Hello and welcome to the forum!
To solve this problem, we can use the equation for projectile motion:
Yf = Yi + Vyi*t - 1/2*g*t^2
We know that the initial vertical velocity (Vyi) is 0, since the crate is initially only moving horizontally. Therefore, the equation becomes:
Yf = Yi - 1/2*g*t^2
Plugging in the values given in the problem, we get:
0 = 10100 - 1/2*9.81*t^2
Solving for t, we get t = 45.22 seconds.
Therefore, it will take approximately 45 seconds for the crate to hit the ground.

Hope this helps!