# A little boy jumps onto a small merry-go-round(radius 2.00m) in a park that rotates for 2.30s through an arc length of 2.55 before coming to rest. If he landed( and stayed at a distance of 1.75 , frp, tje cemtral axis of rotation of the merry-go-round, what was his average angular speed and average tangential speed?

I got one answer and that is v=1.11m/s but I cant get the other answer.

## angular ... 2.55 rad / 2.30 s

## I think the arc length is the distance along the circumference here.

r theta = 2.55

theta = 2.55/2 = 1.275 radians

so I get

omega = 1.275/2.30 = 0.554 radians/second

he went from 0 to 0.554 rad/s so his average omega is 0.277 rad/s

so v = omega r

= 0.277 * 1.75 = 0.485 meters/s

## To find the average angular speed, we can use the formula:

angular speed = (arc length) / (time)

angular speed = 2.55m / 2.30s

angular speed ≈ 1.1087 rad/s

Since the boy landed at a distance of 1.75m from the central axis of rotation, we can find the average tangential speed using the formula:

tangential speed = (angular speed) x (radius)

tangential speed = 1.1087 rad/s x 2.00m

tangential speed ≈ 2.2174 m/s

Therefore, the average angular speed is approximately 1.1087 rad/s and the average tangential speed is approximately 2.2174 m/s.

## To find the average angular speed and average tangential speed of the little boy, we can use the formulas:

Angular speed (ω) = Δθ/Δt

Tangential speed (v) = ω * r

Given data:

Radius of the merry-go-round (r) = 2.00 m

Time taken for the merry-go-round to rotate (Δt) = 2.30 s

Arc length covered (Δθ) = 2.55 m

Distance from the central axis of rotation (d) = 1.75 m

First, let's find the angular speed (ω):

Angular speed (ω) = Δθ/Δt

Substituting the values:

ω = 2.55 m / 2.30 s

Calculating:

ω ≈ 1.11 rad/s

Next, let's find the tangential speed (v):

Tangential speed (v) = ω * r

Substituting the values:

v = (1.11 rad/s) * (2.00 m)

Calculating:

v ≈ 2.22 m/s

Therefore, the average angular speed is approximately 1.11 rad/s, and the average tangential speed is approximately 2.22 m/s.

It seems like your calculation for the average tangential speed (v) is incorrect. The correct value should be 2.22 m/s, not 1.11 m/s.