A 62 kg water skier, moving at 14 m/s , lets go of the towline.
a.Find her momentum. 868kgm/s
b.What impulse is needed to bring her to rest? -868Ns
c.If the water exerts an average force of -275 N on the skier, how long must the force act? 3.16 s
d.How far does she travel during this time? ??
To determine how far the water skier travels after letting go of the towline, we need to use the kinematic equation that relates distance, initial velocity, final velocity, and time:
d = (v + u) / 2 * t
where d is the distance traveled, u is the initial velocity, v is the final velocity, and t is the time.
In this case, the skier comes to rest (final velocity = 0), and the initial velocity is known (u = 14 m/s). The time is not given, but we will use the information from part (c) of the question, which states that the water exerts an average force of -275 N on the skier.
To find the time, we can use the definition of impulse:
Impulse = Force * time
Given that the impulse needed to bring the skier to rest is -868 Ns (as mentioned in part (b)), and the average force is -275 N, we can rearrange the formula to solve for time:
time = Impulse / Force
time = (-868 Ns) / (-275 N) = 3.16 seconds
Now we can substitute the values of initial velocity (u = 14 m/s) and time (t = 3.16 s) into the distance formula:
d = (v + u) / 2 * t
d = (0 + 14) / 2 * 3.16
d = 7 / 2 * 3.16
d = 3.5 * 3.16
d = 11.06 meters
Therefore, the water skier travels approximately 11.06 meters during the time it takes for the water to bring her to rest.