The minute hand of a clock is 8 inches long. How far does the tip of the minute hand move in 30 minutes? How far does it move in 20 minutes?
For 30 min. I got 8pie inches. For 20 mins., I got (16pie/3)inches. but i don't know if these answers are correct. if my answers are wrong, please show me the steps to solving this.
Thanks.
Arc distance= radius*angular speed*time
angular speed for a minute hand is 1 rev per hour, or 2PI rad/hr
for 20 min:8in*2PI/hr*1/3 hr
You are correct.
The tip of the minute hand moves 8π inches in 30 minutes and (16π/3) inches in 20 minutes.
To find the distance the tip of the minute hand moves in a certain amount of time, we can use the formula:
Arc distance = radius * angular speed * time
Given that the radius of the minute hand is 8 inches and the angular speed is 2π rad/hr (since the minute hand completes 1 revolution per hour), let's calculate the distances:
For 30 minutes:
Arc distance = 8 inches * (2π rad/hr) * (30 min / 60 min)
Arc distance = 8π inches
For 20 minutes:
Arc distance = 8 inches * (2π rad/hr) * (20 min / 60 min)
Arc distance = 16π/3 inches
So, your answers are correct. The tip of the minute hand moves 8π inches in 30 minutes and 16π/3 inches in 20 minutes.
To find the distance the tip of the minute hand moves in a certain amount of time, we can use the formula:
Arc distance = radius * angular speed * time
In this case, the radius is given as 8 inches.
The angular speed of the minute hand is 1 revolution per hour, or 2π radians per hour.
For 30 minutes:
Arc distance = 8 inches * 2π radians per hour * (30 minutes / 60 minutes per hour)
= 8π inches
So, you are correct that the tip of the minute hand moves 8π inches in 30 minutes.
For 20 minutes:
Arc distance = 8 inches * 2π radians per hour * (20 minutes / 60 minutes per hour)
= 16π/3 inches
Therefore, your answer for the tip of the minute hand moving 16π/3 inches in 20 minutes is correct.