The water skier there has a mass of 71.0 kg. Find the magnitude of the net force acting on the skier when (a) she is accelerated from rest to a speed of 14.0 m/s in 9.00 s and (b) she lets go of the tow rope and glides to a halt in 16.0 s.

Well, it seems like the water skier is in quite a "dilemma" there. Let's see if I can help.

(a) To find the magnitude of the net force acting on the skier when she is accelerated from rest to a speed of 14.0 m/s in 9.00 s, we can use Newton's second law: Fnet = ma.

The skier's initial velocity, v0, is 0 m/s, and her final velocity, vf, is 14.0 m/s. The time taken, t, is 9.00 s. We can calculate the acceleration using the formula:

a = (vf - v0) / t

Calculating this gives us:

a = (14.0 m/s - 0 m/s) / 9.00 s

a = 1.56 m/s^2

Now, we can find the magnitude of the net force using the equation:

Fnet = ma

Fnet = (71.0 kg) * (1.56 m/s^2)

Fnet = 110.76 N

So, the magnitude of the net force acting on the skier when she is accelerated is approximately 110.76 N.

(b) When the skier lets go of the tow rope and glides to a halt in 16.0 s, she experiences a force that opposes her motion, which is essentially the force of friction. The magnitude of this force would be equal to the force needed to slow her down and eventually bring her to rest.

Since the skier comes to a halt, her final velocity, vf, is 0 m/s, and the time taken, t, is 16.0 s. Again, we can use the formula a = (vf - v0) / t, but since vf is 0, we can simplify it to:

a = (0 m/s - 14.0 m/s) / 16.0 s

a = -0.875 m/s^2

Here, the negative sign indicates that the acceleration is opposite to the skier's initial motion.

Now, using Fnet = ma, we can calculate the magnitude of the net force:

Fnet = (71.0 kg) * (-0.875 m/s^2)

Fnet = -62.225 N

Ah, negative force? That means the force is acting in the opposite direction to the motion. So, the magnitude of the net force acting on the skier when she glides to a halt is approximately 62.225 N in the opposite direction.

Hope that helps! Stay "water-ful"!

To find the magnitude of the net force acting on the skier, we need to use Newton's second law of motion, which states that the net force on an object is equal to the product of its mass and acceleration: F = m * a.

(a) When the skier is accelerated from rest to a speed of 14.0 m/s in 9.00 s, we first need to calculate the acceleration. We can use the equation:

a = (vf - vi) / t,

where a is the acceleration, vf is the final velocity, vi is the initial velocity (which is 0 since the skier is at rest), and t is the time.

Plugging in the values, we get:

a = (14.0 m/s - 0 m/s) / 9.00 s = 1.56 m/s^2.

Now, we can calculate the magnitude of the net force:

F = m * a.

F = 71.0 kg * 1.56 m/s^2 = 110.8 N.

Therefore, the magnitude of the net force acting on the skier when she is accelerated from rest to a speed of 14.0 m/s in 9.00 s is 110.8 N.

(b) When the skier lets go of the tow rope and glides to a halt, we need to consider that the acceleration is negative (opposite to the initial direction). We can use the same formula as before:

a = (vf - vi) / t,

where vi is the initial velocity (14.0 m/s) and vf is the final velocity (0 m/s).

Plugging in the values, we get:

a = (0 m/s - 14.0 m/s) / 16.0 s = -0.875 m/s^2.

Now, we can calculate the magnitude of the net force:

F = m * a.

F = 71.0 kg * (-0.875 m/s^2) = -62.125 N.

Note that the negative sign indicates that the force is acting in the opposite direction to the initial motion.

Therefore, the magnitude of the net force acting on the skier when she lets go of the tow rope and glides to a halt in 16.0 s is 62.125 N.