# Kinematics in 2d, plane drops an object

• FlukeATX
In summary, the problem involves finding the time and height of a radar decoy released from an airplane diving at an angle of 28.0° below the horizontal. The horizontal distance between the release point and the point of impact is 777 m. Using the known values of speed, angle, and distance, the time the decoy is in the air can be calculated. However, upon submission, the answer was incorrect and further checking revealed a unit inconsistency.
FlukeATX

## Homework Statement

A certain airplane has a speed of 267.2 km/h and is diving at an angle of θ = 28.0° below the horizontal when the pilot releases a radar decoy (Fig. 4-37). The horizontal distance between the release point and the point where the decoy strikes the ground is d = 777 m. (a) How long is the decoy in the air? (b) How high was the release point?

d=Vi*t+1/2a(t^2)

## The Attempt at a Solution

Okay, step one is to find the velocity in the x and y directions, here is my attempt:
Vy=sin(-28)*267.2= -125.4428016
Vx=cos(-28)*267.2= 235.9235968

So we have the following knowns:
V=267.2m/s
Vy=-125.4428016m/s
Vx=235.9235968m/s
Dx=777m
Ax=0
Ay=-9.8m/s^2
Dy=?
T=?

Okay, cool, plenty of information. Let's solve for T first so we can find Dy afterwards:
Dx=VxT + 1/2Ax(T^2)
777=(235.9235968)(T) + (1/2)0(T^2)
777=(235.9235968)(T) + 0
T=777/(235.9235968)
T=3.293439107

----STOP----
Now at this point, I went on to solve for Dy, but we're going to stop here for the following reason: when I submitted my answer for T to the wileyplus online system, it told me my answer was wrong. What did I do wrong? Everything seems to make sense. Please help!

The speed of the airplane is given in km/hr. You should check for consistency in your units ;)

Ah jeez, totally overlooked that. Thanks for the help!

## What is kinematics in 2d?

Kinematics in 2d is the branch of physics that studies the motion of objects in a two-dimensional plane. It involves analyzing the position, velocity, and acceleration of objects without considering the forces that cause the motion.

## How is kinematics in 2d used to describe the motion of a plane dropping an object?

Kinematics in 2d can be used to describe the motion of a plane dropping an object by analyzing the position, velocity, and acceleration of the object as it falls. This can help determine how far the object will fall, how fast it will fall, and how its speed changes over time.

## What factors affect the motion of an object in a plane drop?

The factors that affect the motion of an object in a plane drop are the initial position and velocity of the object, the force of gravity, and any air resistance or drag acting on the object.

## How does acceleration due to gravity impact the motion of an object in a plane drop?

Acceleration due to gravity, which is constant at 9.8 m/s² on Earth, causes objects to accelerate towards the ground as they fall. This acceleration increases the object's velocity and decreases its position over time.

## Can kinematics in 2d be used to predict the exact behavior of an object in a plane drop?

No, kinematics in 2d does not account for external factors such as air resistance and turbulence, which can affect the motion of an object in a plane drop. However, it can provide a good approximation and understanding of the object's motion.

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