Linear displacement in a circular motion

[katielynn09]

A flea is at point A on a horizontal turntable
15.7 cm from the center. The turntable is ro-
tating at 30.5 rev/min in the counterclockwise
direction. The flea jumps vertically upward to
a height of 5.18 cm and lands on the turntable
at point B. Place the coordinate origin at the
center of the turntable with the positive x axis
fixed in space and initially passing through A.
The acceleration of gravity is 9.8 m/s2 .
Find the linear displacement of the flea.
Answer in units of m.

I found the angle through which point A has rotated when the flea lands to be 37.63118767 degrees.

how would i find the displacement?

i tried finding the other angles by taking 180-36.63... and / 2 and then using the law of sines but it didn't work.

 

[Jhero]

you can use the basic principles of kinematics to find the displacement of the flea on the turntable. First, let's label the given information on a diagram:

Point A: 15.7 cm from the center of the turntable
Point B: vertical displacement of 5.18 cm
Rotation rate: 30.5 rev/min in the counterclockwise direction

We can use the formula for angular velocity (ω = Δθ/Δt) to find the angle through which point A has rotated when the flea lands:

ω = (30.5 rev/min) (2π rad/rev) = 61π rad/min

Δθ = ωΔt = (61π rad/min) (1 min/60 s) = 61π/60 rad ≈ 1.016 rad

Now, we can use the law of cosines to find the length of the displacement vector from A to B:

c² = a² + b² - 2ab cos(θ)
c² = (15.7 cm)² + (5.18 cm)² - 2(15.7 cm)(5.18 cm) cos(1.016 rad)
c = 16.02 cm ≈ 0.1602 m

Therefore, the linear displacement of the flea on the turntable is approximately 0.1602 m.