A parachutist bails out and freely falls 64.7 m. Then the parachute opens and thereafter she decelerates at 1.88 m/s2. She reaches the ground with a speed of 3.07 m/s. What is her average speed (in m/s) for the fall?
I was planning on finding the time before she decelerated using x=v0t - (1/2)at^2, where x=64.7m, a=-9.8m/s^2(because of gravity during free fall), v0 = 0m/s and solving for t1. Now to find the time she falls after she decelerates using vfinal = v0 +at, vfinal = 3.07, a=-1.88, and solving for t2. Then subtracting the two to find delta t.
And to find average speed I would use total distance = 64.7, divided by delta t It doesn't seem to give me the right answer, am I doing everything right?
The approach you described to find the average speed is correct. However, there seems to be a small error in the calculation of the time after deceleration. Let's go through the steps to find the average speed for the fall:
Step 1: Finding the time before deceleration:
Using the kinematic equation x = v0t + (1/2)at^2, where x = 64.7m, v0 = 0m/s, and a = -9.8m/s^2 (acceleration due to gravity), we can solve for t1. Plugging in these values, we get:
64.7 = 0*t1 + (1/2)(-9.8)t1^2
Rearranging the equation gives us a quadratic equation:
4.9t1^2 = 64.7
Solving for t1 yields:
t1 = sqrt(64.7 / 4.9) ≈ 3.22 seconds
Step 2: Finding the time after deceleration:
Using the equation v = v0 + at, where v = 3.07m/s, v0 = 0m/s, and a = -1.88m/s^2, we can solve for t2. Plugging in these values, we get:
3.07 = 0 + (-1.88)t2
Solving for t2 yields:
t2 = 3.07 / (-1.88) ≈ -1.63 seconds
This negative result indicates that the parachutist does not spend any time after deceleration. Therefore, the parachutist reaches the ground immediately after decelerating.
Step 3: Calculating the total time (delta t):
To find the total time of the fall, we subtract the time before deceleration from the time after deceleration:
delta t = t1 - t2
= 3.22 - (-1.63)
= 4.85 seconds
Step 4: Calculating the average speed:
The average speed is defined as the total distance traveled divided by the total time taken. In this case, the total distance is given as 64.7m, and the total time is 4.85 seconds. Dividing the distance by the time gives:
Average speed = 64.7m / 4.85s ≈ 13.35 m/s
So, the average speed for the parachutist's fall is approximately 13.35 m/s.