A model airplane of mass 0.9 kg is attached

to a horizontal string and flies in a horizontal circle of radius 5.2 m, making 1.2 revolutions
every 8 s. (The weight of the plane is balanced
by the upward “lift” force of the air on the
wings of the plane.)
The accelaration due to the gravity is 9.81
m/s2.
Find the speed of the plane

Huh ?

it is going (1.2 * 2 pi r) meters in 8 seconds

speed = distance/time = (1.2*2*pi*5.2)/8

To find the speed of the plane, we need to use the formula for centripetal acceleration:

a = (v^2) / r

Where:
a is the centripetal acceleration,
v is the speed of the plane,
and r is the radius of the circular motion.

We can also calculate the period of one revolution using the given information that the plane makes 1.2 revolutions every 8 seconds.

Period (T) = Time / Number of Revolutions
T = 8 s / 1.2

Now, let's find the centripetal acceleration:

a = (v^2) / r

Using the formula for centripetal acceleration, we can rearrange the equation to solve for v:

v^2 = a * r

Now, substituting the known values:

v^2 = (9.81 m/s^2) * 5.2 m

Next, we can take the square root of both sides to solve for v:

v = sqrt((9.81 m/s^2) * 5.2 m)

Calculating the value:

v ≈ sqrt(51.01)
v ≈ 7.14 m/s

Hence, the speed of the plane is approximately 7.14 m/s.