Lecture 4: 3D Kinematics - Free Falling Reference Frames
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1. Shape of the Projectile Trajectory:
Professor Lewin reviews the equations for projectile motion, showing that the trajectory is a parabola. He derives formulas for the highest point (maximum height), the time to reach the highest point, the time of flight (until impact), and the horizontal distance traveled. For given initial speed (speed is a scalar, velocity is a vector), an object thrown at 45 degrees from the vertical will go the farthest.
2. How to Measure the Initial Speed?
An object is shot upwards from a gun-like device. By measuring the height that it reaches, we can find the initial speed. Uncertainties in the results are discussed and are taken into account in the demonstrations that follow.
3. Shoot a Ball for Maximum Horizontal Distance:
The ball is shot at an angle of 45 degrees from the vertical (the uncertainty in the angle is estimated to be about 1 degree). Professor Lewin predicts where the ball will hit the long desk in the lecture hall. He takes into account the uncertainty in the initial speed of the ball and the 1 degree uncertainty in the angle. He marks the locations between which the ball should hit. He then shoots the ball, and indeed it lands as predicted.
4. Shoot a Ball at 30 and 60 Degrees:
For given initial speed, the horizontal range is the same for angles of 30 and 60 degrees from the vertical (but the ball travels higher for 60 degrees -- which of these trajectories takes the longest?). Professor Lewin sets the angle at 30 degrees, and predicts where the ball will hit. He takes the uncertainties into account. The ball lands as predicted.
5. Shoot a Ball at a Monkey Doll:
Someone shoots a ball and aims straight at a monkey who is hanging in a tree. Gravitational acceleration curves the ball's trajectory substantially, and there is no danger that the monkey will get hit. However, tragically the monkey sees the light flash of the gun and he lets go. He falls to the ground, and ... the ball hits the monkey independent of the initial speed of the ball (provided the speed is high enough to reach the tree).
6. Reference Frame of the Falling Monkey:
Both the monkey and the ball are falling with the same gravitational acceleration. From the monkey's point of view (its reference frame) the ball is coming straight at it (no curved trajectory).
7. Professor Lewin (Dressed in Safari Outfit) Fires the Gun
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