Calculating Distance and Velocity in Two-Dimensional Kinematics

In summary, the conversation discusses a problem involving an airplane with specific speed, altitude, and angle of ascent. The goal is to calculate the distance and angle of the package released from the plane. The answers are provided, but the person is seeking help on how to solve the problem. They are advised to use trigonometry to calculate the distance and angle.
  • #1
goj2
3
0
Ive been trying to get this problem. I already have the answers but I want to know how to solve it.

An airplane with a speed of 77.5 m/s is climbing upward at an angle of 34.1 ° with respect to the horizontal. When the plane's altitude is 585 m, the pilot releases a package. (a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the earth. (b) Relative to the ground, determine the angle of the velocity vector of the package just before impact.

The answers are:
(a)1040 m
(b)-61.0°

Can someone help me?
 
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  • #2
what have you done so far??
 
  • #3
goj2: a) work out how long the package will take to fall 585m. Then multiply the answer by the forward speed of the aircraft, worked out using trigonometry. b) is more trigonometry based on the forward speed and the vertical speed.
 

1. What is kinematics in two dimensions?

Kinematics in two dimensions is a branch of physics that studies the motion of objects in two-dimensional space. It involves analyzing the position, velocity, and acceleration of objects as they move in two perpendicular directions.

2. How is velocity calculated in two dimensions?

In two-dimensional kinematics, velocity is calculated by dividing the change in an object's position by the change in time. It is a vector quantity and includes both magnitude (speed) and direction.

3. What is projectile motion?

Projectile motion is the motion of an object that is propelled into the air and then moves under the influence of gravity alone. It is a two-dimensional motion that can be analyzed using kinematic equations.

4. What is the difference between displacement and distance?

Displacement refers to the straight-line distance between an object's starting point and ending point, taking into account its direction. Distance, on the other hand, refers to the total path length an object has traveled, regardless of its direction.

5. How do we analyze motion in two dimensions?

Motion in two dimensions can be analyzed using kinematic equations, which are based on the principles of displacement, velocity, and acceleration. By plugging in known values and solving for unknowns, we can determine the motion of an object in two-dimensional space.

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