a sky diver jumps out of a plane that is 3000m above ground with an initial upward speed of 6m/s she free falls for 20s (assume there is no wind at this time)before pulling the cord to activate the parachute she then falls to the ground at a constant downward speed of 5m/s, how far did she fall before activating the parachute, and how long was she in the air altogether from the moment she left the plane to the moment she touched the ground
Let us divide the ques into 3 parts: the initial v,the 20s descent,the final v,since distance from ground level=3000m.
Let us divide the ques into 3 parts: the initial v,the 20s descent,the final v,since distance from ground level=3000m,
the 1st part:using V=6 v*v/2g=h,36/20=1.8m,new distance(diver) from ground=3000+1.8=3001.8m.
2nd part:20s descent. using a=v-u/t,where a=10.t=20,and u=0,v=200,using v*v/2g=h,200*200/20=2000new h=3001.8-2000
Since final h=1001.8m,find the time,t=h/v, 1001.8/5m/s=200.36.total time=200.36+20+0.6=220.96get 0.6 from h=1.8
To determine the distance the skydiver fell before activating the parachute, we can calculate the total distance covered during free fall. During this period, the skydiver is accelerating downwards due to gravity, and her initial upward speed of 6 m/s is gradually reduced until she reaches a downward speed of 0 m/s.
We can use the following formula to calculate the distance covered during free fall:
d = ut + (1/2)at^2
Where:
d = distance covered
u = initial velocity
t = time
a = acceleration
Given:
Initial upward speed (u) = 6 m/s
Time during free fall (t) = 20 s
Acceleration due to gravity (a) = -9.8 m/s^2 (negative since it acts downwards)
Let's substitute these values into the formula:
d = (6 m/s)(20 s) + (1/2)(-9.8 m/s^2)(20 s)^2
Simplifying the equation:
d = 120 m - (1/2)(9.8 m/s^2)(400 s^2)
d = 120 m - 0.5(9.8 m/s^2)(400 s^2)
d = 120 m - 0.5(9.8 m/s^2)(160,000 s^2)
d = 120 m - 7,840,000 m^2/s^2
Since we're only interested in the distance covered in meters, we can ignore the term in m^2/s^2 since it represents the acceleration due to gravity over time.
d ≈ 120 m
Therefore, the skydiver fell approximately 120 meters before activating the parachute.
To determine the total time in the air, we need to consider both free fall and the descent under the parachute.
The total time in the air from the moment she left the plane to the moment she touched the ground is:
Total time = time during free fall + time during descent under parachute
Given:
Time during free fall = 20 s
Constant downward speed during descent = 5 m/s
To find the time during descent under the parachute, we divide the distance covered (120 m) by the constant downward speed (5 m/s):
time during descent = distance covered / constant downward speed
time during descent = 120 m / 5 m/s
time during descent = 24 s
Now we can calculate the total time in the air:
Total time = 20 s + 24 s
Total time ≈ 44 s
Therefore, the skydiver was in the air for approximately 44 seconds from the moment she left the plane to the moment she touched the ground.