A relief airplane is delivering a food package to a group of people stranded on

Question

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 so that the package lands on a site close to the people. The airplane flies horizontally at a constant altitude 500m directly over the island and the dropped package successfully lands on the site.

1)What is the velocity of the plane if the pilot successfully drops the package from a horizontal distance, D, equal to 600 m from the site
2) Find the magnitude and direction of the velocity of the package when it lands on the site.

Explanation / Answer

take help The key is to realize that in the vertical direction the object has zero initial velocity. The equation needed is: yf = yi + vi*t + 1/2*a*t^2 where yf and yi are initial and final elevations, vi is initial velocity (zero in this case), and a is acceleration, in this case gravity. Make your point of zero altitude your origin, with the positive direction pointing up (this means yf = 0, and acceleration has to be taken as NEGATIVE when you plug it in because gravity acts downward). Plug in your numbers and solve for t. B) The important thing to note here is that the acceleration in the horizontal direction is zero for projectile motion problems, and the initial velocity is the same as that of the plane. So again your equation is: xf = xi + vi*t +1/2*a*t^2 where vi this time refers to the speed of the plane. Taking your horizontal origin to be at the point of release (xi = 0) and simplifying gives xf = vi*t You know t from part A, plug in and solve. C) Now that you know everything, this is the easiest part. Acceleration is simply change in velocity over time. Your governing equation (in the vertical direction, which is what the question is asking) is: vf = vi + a*t where vi =0 (vertical direction). Direction does not matter in this particular case, so take gravity to be positive.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.