Physics Chapter 3

What angle θ0 produces the longest jump?

45°

True or False: All other things being equal, if the ball is thrown at half the given speed it will travel half as far.

False

True or False: Because the x-component of the displacement doesn't depend explicitly on g, the horizontal distance traveled doesn't depend on the acceleration of gravity.

False

True or False: Neglecting air friction and lift effects, a projectile with a horizontal acceleration always stays in the air longer than a projectile that is freely falling.

False

what is relative velocity

Relative velocity is all about relating the measurements of two different observers, one moving with respect to the other. The measured velocity of an object depends on the velocity of the observer with respect to the object.

Problem If the skipper of the boat of Example 3.8 moves with the same speed of 10 km/h relative to the water but now wants to travel due north, as in Figure 3.16a, in what direction should he head? What is the speed of the boat, according to an observer on the shore? The river is flowing east at 5 km/h. The speeds in this example are the same as in Example 3.8. Why isn't the angle the same as before?

The angle is different because relative velocity depends on both the magnitude and the direction of the velocity vectors. In Example 3.9, the boat's velocity vector forms the hypotenuse of a right triangle, whereas in Example 3.8, that vector forms a leg of a right triangle.

Problem An Alaskan rescue plane drops a package of emergency rations to stranded hikers, as shown in Figure 3.10. The plane is traveling horizontally at 40 m/s at a height of 1x10^2m above the ground. Neglect air resistance. Where does the package strike the ground relative to the point at which it was released? What are the horizontal and vertical components of the velocity of the package just before it hits the ground? What is the angle of the impact? Neglecting air resistance effects, what path does the package travel as observed by the pilot? Explain.

To the pilot, the package appears to drop straight down because the x-components of velocity for the plane and package are the same.

What is projectile motion?

objects that move in both the x- and y-directions simultaneously under constant acceleration. An important special case of two-dimensional motion