(COLLAB) Simulate the motion of an idealized projectile in PhysLab. What is the range of the shuttlecock launched with an initial speed of 7.2223 m/s at 40.2526-degree angle with respect to the horizontal from a height of 2.33 m in a planet where the downward gravitational acceleration has a magnitude of 9.5241 m/s2?

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.

In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?

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?