Finding Time for Package to Reach Sea Level from Ejection?

[atbruick]

Homework Statement

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 700 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.

After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 260 mph in the horizontal direction.

Homework Equations

yfinal=yinitial+vinitial*t-.5gt^2

The Attempt at a Solution

Hoping my substitutions are right, I got an equation of 0=700+260t-.5(9.80)t^2, and got an answer of 196; I know I'm doing something wrong to find t because it said my answer of 196 seconds is wrong, I just can't figure out how to correctly find t. Should I factor it out?

 

[PhanthomJay]

Same error as in the other problem. What is the initial speed in the y direction? And watch your units! I don't know why problems give units in both systems of measure; I guess to check your knowledge of conversion factors.

 

[atbruick]

ok thank you, I got a correct time of 12 seconds, then was asked to find the distance from the plane to the island if I wanted to release it so it would land on the island, and got 1390m. Now I'm being asked to find the final speed of the package when it hits the ground. How do you know whether to select the equation from horizontal or vertical motion? I want to say vertical but I'm not positive.

 

[PhanthomJay]

You have to look in both directions. Just when the package hits the ground, it has an x component of its final velocity, and a y component of its final velocity. Solve for both to find the resultant velocity (and speed) by using a well known theorem. (You can also use energy methods, but I assume you're not on that page... yet).

 

[atbruick]

oh so it's like solving vectors? by finding the xvector component and yvector component and then using Pythagorean theorem to find the final velocity?

 

[PhanthomJay]

oh so it's like solving vectors? by finding the xvector component and yvector component and then using Pythagorean theorem to find the final velocity?

That's right, the velocity is a vector, and its magnitude is its speed, a scalar quantity. Once you get into energy methods, you can calculate its final speed directly without determining the velocity, but for now, continue as you have stated.

 

[atbruick]

Thank you