Karen is running forward at a speed of 9 m/s. she tosses her sweaty headband backward at a speed of 20 m/s. the speed of the headband, to the nearest whole number relative to a stationary observer watching karen, is m/s

Let Karen's forward speed be considered as positive.
Therefore, before the headband is tossed backward, the speed of the headband is
V = 9 m/s

The headband is tossed backward relative to Karen at a speed of 20 m/s. Therefore the speed of the headband relative to Karen is
U = -20 m/s

The absolute speed of the headband, relative to a stationary observer is
V - U
= 9 + (-20)
= - 11 m/s

The stationary observes the headband traveling (in the opposite direction to Karen) at a speed of 11 m/s backward.

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.

It equals just about 6,300 km per hour each day an week