Question

Will fan and medal
Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle.

Part 1: How many radians does the minute hand move from 3:35 to 3:55? (Hint: Find the number of degrees per minute first.)
Part 2: How far does the tip of the minute hand travel during that time?
Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 3π inches?
Part 4: What is the coordinate point associated with this radian measure?

Answer 1

I just need to know if I'm right. To find the degree you would divide the degrees of a circle by the number of minutes in an hour which would be 360/60=6. So six per minute you would multiply by 5 and get 30° in 5 minutes. Now we need to find the radians by dividing 30 by 180 like this 30/180 which would give you 1/6 and the radian measure is π/6. I'm not exactly sure what to do now

Answer 2

@texaschic101 can you help?

Answer 3

@Michele_Laino can you help? Please.

Answer 4

Can someone help?

Answer 5

the angular velocity of the 4-inch hand is
2*pi/60= pi/30 radians/min

Answer 6

I'm confused..

Answer 7

since the long minute hand travels one complete turn every 60 minutes

Answer 8

so we can write this condition:
\[2\pi R = \omega R\Delta t\]
where \Delta t = 60 minutes and R = 4 inches

Answer 9

\[2\pi R = \omega R60\]
dividing by 60, we get:
\[\omega = \frac{{2\pi }}{{60}} = \frac{\pi }{{30}}\]

Answer 10

so the answer for part 1, is:

\[\alpha = \frac{\pi }{{30}} \times 20\]

Answer 11

since from 3.35 to 3.55 there are 20 minutes

Answer 12

so, after a simplification, we get:
\[\alpha = \frac{{2\pi }}{3}\]

Answer 13

oops..
\[\alpha = \frac{{2\pi }}{3}\;radians\]

Answer 14

Sorry my computer froze. I think I am understanding a bit more

Answer 15

now, part 2
the requested distance L, is given by the subsequent computation:
\[\Large L = R\alpha = R\frac{{2\pi }}{3}\]
where R = 4 inches

Answer 16

The part I need help with is part 4 now

Answer 17

part 3)
the requested angle is:
\[\Large \beta = \frac{{3\pi }}{R}\]

Answer 18

and the requested coordinates are:
\[\Large \left( {R,\frac{{3\pi }}{2}} \right)\]