Example 1 Projectile Motion
A plane at a constant altitude of 1050 m and traveling at a speed of 115 m/s in the +x direction drops a crate that plummets to the Earth. Determine final velocity, total time, and final x position. Assume +y is upwards and +x is parallel to the plane's initial velocity. Don't forget about the age old question of What should reactants have for reactions to occur?
+yWe also discuss several other topics like a mental shortcut that helps us to streamline our thinking
Don't forget about the age old question of Can our senses be detectives?
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We also discuss several other topics like What is the standard formula in solving for arc length?
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1) Between the x and y directions we know that one variable will remain the same time.
So first solve for time.
2) More Y components are known than X, so let's solve for t in the y direction.
3) Now that we know t, we can solve for
4) To find , we must use its components.
We already know , so we must calculate
5) Use to solve for . Pythagorean theorem.
⤷ a special case in 2D motion.
Velocity Tangent to circle/arc of motion and constantly changing direction
Acceleration Perpendicular to circle/arc of motion toward the center
Relative Motion (1D)
When there are multiple observers, we often indicate the reference frame in the subscript.
→ velocity of object A relative to observer B
Ex. Consider an observer in a vehicle and an observer on the road, both observing another car.
Car A ⇒ 40 m/s “I think car B is moving at 30 m/s”
Car B ⇒ 70 m/s “No way! It’s traveling 70 m/s for sure!”
Converting between reference frames
A plane is headed North according to its compass and flies with an airspeed of 240 km/hr
A cross wind at 100 km/h from west to east pushes the plane sideways
Velocity of the plane relative to earth is