Answer to Question #203952 in Physics for Rethabile

Question

17. An electronic advertising sign repeats a message every 7 seconds, day and night, a week. How many times did the message appear on the sign? (4)

A) 9 x 104 message/week

B) 10 message/week

C) 1.689 x 104 message/week

D) 459 x 104 message/week

E) 105 message/week

 

18. A highway is to be built between two towns, one of which lies 18.0 km South and 85.0 km West of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due West? (4)

A) 86.9 km; 12.0o S of W C) 78 km; 90o N of E E) 10 km; 120o E of N

B) 103 km; 120o E of W D) 0 km; 0o S of W

19. Which of the following quantities have the dimensions of the speed? (2)

A) at2 C) 2at 

B) a2t D) (2ax)1/2

Answer 1

17. Find the number of seconds in a week:

$$T=3600·24·7=604800\text{ s}.$$

Since each message takes 7 seconds, the number of messages is

$$n=604800/7=86400.$$

The closest answer is 9·10⁴ times a week.

18. The shortest way can be found by Pythagorean theorem:

$$d=\sqrt{18^2+85^2}=86.9\text{ km}.$$

The angle is

$$\theta=\arctan\frac{18}{85}=12°.$$

19. The following quantities have the dimensions of the speed:

$$(2ax)^{1/2}, \space\space\space2at.$$