An airplane is supposed to fly with a velocity vector of \( \langle 160,-120\rangle \), but a steady wind has a velocity vector of \( \langle 40,40\rangle \). How much does the wind speed affect the plane's intended velocity vector?

7. Die grosse Rolltreppe im Einkaufszentrum ist 28.8 m lang und bewegt sIch mit \( 1.6 \mathrm{~m} / \mathrm{s} \). Maria rennt aber lieber mit \( 2.4 \mathrm{~m} / \mathrm{s} \) die Treppe hoch, die parallel dazu verläuft. Ihr Bruder Remo nimmt die Rolltreppe. a) Wie viele Sekunden Vorsprung muss sie Remo lassen, damit sie gleichzeitig oben ankommen? b) Wie schnell wäre sie oben, wenn sie die Rolltreppe hochrennen würde?

Figure 22-44 Problem: 17. Module 22-3 The Electric Field Due to a Dipole (2-18) The electric field of an electric dipole along the dipole axis is approximated by Eqs, \( 22-8 \) and \( 22-9 \). If a binomial expansion is made of Eq. \( 22-7 \), what is the next term in the expression for the di- pole's electric field along the dipole axis? That is, what is \( E_{\text {nex }} \) in the expression \[ E=\frac{1}{2} \frac{q d}{3}+E_{\text {next }} \text { ? } \]

21. A uniform bar \( A B \) of length 6 as been placed on a horizontal smooth table of width \( 5 a \) as shown in the figure. Length \( 2 a \) of the bar is overhanging. Mass of the bar is \( 4 m \). An insect of mass \( 3 m \) is sitting at the end \( A \) of the bar. The insect walks along the length of the bar to reach its other end \( B \).

19. The resistance R to the motion of a car is partly constant and party proportional to the square of the speed V . When the speed is \( 30 \mathrm{~km} / \mathrm{hr} \), the resistance is 190 N and when the speed is \( 50 \mathrm{~km} / \mathrm{hr} \), the resistance is 350 N . Find for what speed the resistance is 302.5 ohms. (WAEC)

3. Solve the problem analytically, deriving any necessary formulas not provided in the textbook. Ensure all steps and reasoning are clearly shown. 4. \( \mathrm{g}=9.8 \mathrm{~m} / \mathrm{s} 2 \) A 0.0450 kg golf ball initially at rest is given a speed of \( 24.9 \mathrm{~m} / \mathrm{s} \) when a club strikes it. If the club and ball are in contact for 2.40 ms , what average force acts on the ball? Is the effect of the ball's weight during the time of contact significant? Why or why not?