4.12 - Interactive checkpoint: clown cannon

A clown in a circus is about to be shot

out of a cannon with a muzzle velocity

of 15.2 m/s, aimed at 52.7° above the

horizontal. How far away should his

fellow clowns position a net to ensure

that he lands unscathed? The net is

at the same height as the mouth of

the cannon.

Answer:

ǻx = m

4.13 - Interactive problem: test your juggling!

Much of this chapter focuses on projectile motion: specifically, how objects move in

two dimensions. If you have grasped all the concepts, you can use what you have

learned to make the person at the right juggle.

The distance between the juggler’s hands is 0.70 meters and the acceleration due

to gravity is í9.80 m/s^2. You have to calculate the initial x and y velocities to send

each ball from one hand to the other. If you do so correctly, he will juggle three balls

at once.

There are many possible answers to this problem. A good strategy is to pick an

initial x or y component of the velocity, and then determine the other velocity

component so that the balls, once thrown, will land in the juggler’s opposite hand.

You want to pick an initial y velocity above 2.0 m/s to give the juggler time to make

his catch and throw. For similar reasons, you do not want to pick an initial x velocity

that exceeds 2.0 m/s.

Make your calculations and then click on the diagram to the right to launch the

simulation. Enter the values you have calculated to the nearest 0.1 m/s and press

the GO button. Do not worry about the timing of the juggler’s throws. They are calculated for you automatically.

If you have difficulty with this problem, refer to the sections on projectile motion.

4.14 - Reference frames

Reference frame: A coordinate system used to

make observations.

The choice of a reference frame determines the perception of motion. A reference

frame is a coordinate system used to make observations. If you stand next to a lab table

and hold out a meter stick, you have established a reference frame for making

observations.

The choice of reference frames was a minor issue when we considered juggling: We

chose to measure the horizontal velocity of a ball as you saw it when you stood in front

of the juggler. The coordinate system was established using your position and

orientation, assuming you were stationary relative to the juggler.

As the juggler sees the horizontal velocity of the ball, however, it has the same

magnitude you measure, but is opposite in sign. It does so because when you see it

moving from your left to your right, he sees it moving from his right to his left. If you measure the velocity as 1.1 m/s, he measures it as

í1.1 m/s.

In the analysis of motion, it is commonly assumed that you, the observer, are standing still. To pursue this further, we ask you to sit or stand

still for a moment. Are you moving? Likely you will answer: “No, you just asked me to be still!”

That response is true for what you are implicitly using as your reference frame, your coordinate system for making measurements. You are

implicitly using the Earth’s surface.

But from the perspective of someone watching from the Moon, you are moving due to the Earth’s rotation and orbital motion. Imagine that the

person on the Moon wanted to launch a rocket to pick you up. Unless the person factored in your velocity as the Earth spins about its axis, as

well as the fact that the Earth orbits the Sun and the Moon orbits the Earth, the rocket surely would miss its target. If you truly think you are

Reference frames

System for observing motion

(^78) Copyright 2000-2007 Kinetic Books Co. Chapter 04