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- Check Your Understanding A boat heads north in still water at 4.5m/s directly across a river that is running east at 3.0 m/ s. What is the velocity o the boat with respect to Earth?Raindrops fall vertically at 43 m/s relative to the earth. What does an observer in a car moving at 22.0 m/s a straight line measure as the velocity of the raindrops?Check Your Understanding If the two golf shots in Example 4.9 were bunched at the same speed, which shot would have the greatest range? When we speak of the range of a projectile on level ground, we assume R is very small compared with the circumference of Earth. If, however, the range is large, Earth curves away below the projectile and the acceleration resulting from gravity changes direction along the path. The range is larger than predicted by the range equation given earlier because the projectile has father to fail than it would on level ground, as shown in Figure 4.17, which is based on a drawing in Newton’s Principia. If the initial speed is great enough, the projectile goes into orbit. Earth’s surface drops every 8000 m. In 1 s an object falls 5 m without a resistance. Thus, if an object is given a horizontal velocity of 8000 m/s (or 18,000 mi/hr) near Earth’s surface, it will go into orbit around the planet because, the surface continuously falls away from object Thu is roughly the speed of the Space Shuttle in a low Earth orbit when it was operational, or any satellite in a low Earth orbit. These and other aspects of orbital motion, such as Earth’s rotation, are covered in greater depth in Gravitation. Figure 4.17 Projectile to satellite. In each case shown here, a projectile is launched from a very high tower to avoid air resistance. With increasing initial speed, the range increases and becomes longer than t would be on level ground because Earth curves away beneath its path. With a speed of 8000 m/s, orbit is achieved.
- Drew Brees of the New Orleans Saints can throw a football 23.0 m/s (50 mph). If he angles the throw at 10 from the horizontal, what distance does it go if it is to be caught at the same elevation as it was thrown?Check Your Understanding An airplane lands on a runway traveling east. Describe its acceleration.Check Your Understanding If Trooper runs 20 m west before taking a rest, what is his displacement vector?
- In 2007, Michael Carter (U.S.) set a world record in theshot put with a throw of 24.77 m. What was the initial speedof the shot if he released it at a height of 2.10 m and threw itat an angle of 38.0º above the horizontal? (Although themaximum distance for a projectile on level ground is achievedat 45º when air resistance is neglected, the actual angle toachieve maximum range is smaller; thus, 38º will give alonger range than 45º in the shot put.)A projectile is shot at ahill, the base of which is 300 m away. Theprojectile is shot at 60°above the horizontalwith an initial speed of 75 m/s. The hill can beapproximated by a plane sloped at to thehorizontal. Relative to the coordinate systemshown in the following figure, the equation ofthis straight line is y= (tan 20°) x−109 in SIunits. Where on the hill does the projectileland? How long does the trip take?Do I calculate A & B's velocity that +ve or -ve in opposite direction?
- A projectile is lauched horizontally from the top edge of a 20 m tall building with a Vox of 25 m/s. What is its intial velocity along the x axis?an albatrossglides at a constant 15 m/s horizontallyabove level ground, moving ina vertical plane that contains theSun. It glides toward a wall of heighth = 2.0 m, which it will just barelyclear. At that time of day, the angleof the Sun relative to the ground isu = 30. At what speed does theshadow of the albatross move (a) across the level ground andthen (b) up the wall? Suppose that later a hawk happens to glidealong the same path, also at 15 m/s.You see that when its shadowreaches the wall, the speed of the shadow noticeably increases.(c) Is the Sun now higher or lower in the sky than when the albatrossflew by earlier? (d) If the speed of the hawk’s shadow onthe wall is 45 m/s, what is the angle u of the Sun just then?Agent Bond is standing on a bridge, 15 m above the roadbelow, and his pursuers are getting too close for comfort.He spots a flatbed truck approaching at 25m/s which hemeasures by knowing that the telephone poles the truck ispassing are 25 m apart in this region. The roof of the truckis 3.5 m above the road, and Bond quickly calculates howmany poles away the truck should be when he drops downfrom the bridge onto the truck, making his getaway. Howmany poles is it?