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Dorothy's dog, Toto, is tied to a stake in the middle of her yard. Toto likes to run in circles around the stake at the end of a 25-foot chain. Toto can complete 2.5 rotations in 26 seconds.

A. What is the DISTANCE that Toto covered in 2.5 circles (feet)?
B. What was the SPEED that Toto was traveling (mph)?
C. What is Toto's DISPLACEMENT distance (feet)?
D. What DIRECTION was the displacement distance in (degrees)?
E. What was Toto's VELOCITY (feet per second)?

User Ctrl S
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Final answer:

Toto covered a distance of 125π feet in 2.5 circles around the stake. His speed was approximately 12.08 feet per second. Toto's displacement was zero feet and his velocity was also zero feet per second.

Step-by-step explanation:

To find the distance Toto covered in 2.5 circles, we need to calculate the circumference of the circle. The formula for the circumference is C = 2πr, where r is the radius. Since Toto is tied to a stake with a 25-foot chain, the radius is 25 feet. Therefore, the circumference of the circle is C = 2π(25) = 50π feet. To find the distance, we multiply the circumference by the number of circles Toto completed: 50π * 2.5 = 125π feet.

To find the speed at which Toto was traveling, we divide the distance (125π feet) by the time (26 seconds): Speed = Distance / Time = 125π / 26 ≈ 12.08 feet per second.

Since Toto completed 2.5 circles, his displacement is zero. Displacement represents the shortest distance from the starting point to the final position, regardless of the path taken. In this case, Toto returned to the starting point, so his displacement is zero feet.

Since Toto's displacement is zero, the direction of the displacement is also zero degrees. Displacement does not have a direction when it is zero.

Toto's velocity can be found by dividing the displacement (zero feet) by the time (26 seconds): Velocity = Displacement / Time = 0 / 26 = 0 feet per second.

User Ctuffli
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