Alex is exploring a cave that has a slight incline and is iced over, forcing her to use ice cleats to explore it. After climbing 50 m into the cave, she finds what she is looking for and she takes out her ice pick and hammer to begin removing the stones. Little does she know her hammering has triggered a rock slide 100 m into the cave, releasing a large boulder to slide down the icy incline with no friction. The boulder is released from rest and accelerates down toward her at a constant rate of 0.85 m/s2. She doesn’t notice this until the boulder is only 25 m away from her. Reacting quickly, she pushes herself down the incline towards the cave entrance, knowing the boulder is too large to fit through it. Remembering what she learned in physics, she knows she will accelerate down the inline with the same acceleration as the boulder, thanks to the frictionless surface created by the ice.
(d) Now since Alex has escaped the cave, she has a new problem. She is sliding towards a cliff that is 10 m away from the cave entrance. The good news is, she is no longer speeding up, but instead slowing down due to friction. Based on your previous answers, how fast is she moving when she escapes the cave?
(e) Using the fact that the static and kinetic coefficients of friction are 0.75 and 0.5, respectively, will she slow down in time and live or will she plummet to her death? Prove your answer mathematically by showing how far she will slide and compare it to the 10 m mentioned above. And no, you do NOT need to know her mass.
Assume she is sliding on a horizontal surface.
If anyone can help solve or explain the problem, I would greatly appreciate it!
I remember
http://www.jiskha.com/display.cgi?id=1448486880
from before:
She must do 50 meters in 7.67 seconds with starting speed v and acceleration of .85
50 = v (7.67) + (1/2) .85 (7.67)^2
50 - 25 = 7.67 v
v = 3.26 m/s starting speed
NOW ::::::
v = 3.26 + .85 (7.67)
= 9.78 m/s as she pops out into the sun
we need the kinetic friction
work done by friction = initial Ke
mu m g x = (1/2) m v^2
.5 (9.81) x = 9.78^2 / 2
x = 9.75 meter slide
well, she made it !
Thank you so much!!
To solve this problem, we need to use the concept of Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
(d) To find the speed at which Alex is moving when she escapes the cave, we need to determine the distance traveled by the boulder. We already know its acceleration, which is 0.85 m/s^2. We can use the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (which is 0 since the boulder was released from rest), a is the acceleration, and s is the distance traveled.
We can rearrange the equation to solve for v:
v = sqrt(2as)
From the information given, we know that Alex noticed the boulder when it was 25 m away from her and that the boulder initially traveled 100 m from where it was released. So we have:
s = 100 m - 25 m = 75 m
Substituting the values into the equation:
v = sqrt(2 * 0.85 m/s^2 * 75 m)
v = sqrt(127.5 m^2/s^2)
v ≈ 11.3 m/s
Therefore, Alex is moving at approximately 11.3 m/s when she escapes the cave.
(e) To determine if Alex will slow down in time and live or plummet to her death, we need to compare the distance she will slide with the distance to the cliff.
To find the distance Alex will slide before coming to a stop, we can use the equation:
v^2 = u^2 + 2as
where v is the final velocity (which is 0 since she comes to a stop), u is the initial velocity (which is 11.3 m/s), a is the acceleration due to friction, and s is the distance traveled.
We know that the acceleration due to friction can be found using the equation:
F_friction = μ_k * m * g
where μ_k is the coefficient of kinetic friction, m is the mass of the object (which is not needed in this case as per the question), and g is the acceleration due to gravity.
Given that the coefficient of kinetic friction is 0.5, we can calculate the acceleration due to friction:
a = 0.5 * g
We also know that the distance to the cliff is 10 m.
Substituting the values into the equation:
0 = (11.3 m/s)^2 + 2 * (0.5 * g) * s
Simplifying the equation using g = 9.8 m/s^2:
s = (11.3 m/s)^2 / (2 * 0.5 * 9.8 m/s^2)
s ≈ 7.31 m
The calculated distance traveled before Alex comes to a stop is approximately 7.31 m, which is less than the distance to the cliff (10 m). Therefore, she will slow down in time and live.
In summary, Alex will be moving at approximately 11.3 m/s when she escapes the cave, and she will slide a distance of approximately 7.31 m before coming to a stop, which is less than the distance to the cliff (10 m).