A 103kg SWAT team member descends a 27.5m cable attached to a helicopter. If he wishes to reach the bottom in 3.5s, what average force should he apply to the cable?

how do you find the answer

To calculate the average force the SWAT team member should apply to the cable, we can use Newton's second law of motion, which states that force (F) equals mass (m) times acceleration (a):

F = m * a

In this case, the mass of the SWAT team member is given as 103 kg. The acceleration will be the acceleration due to gravity, which is approximately 9.8 m/s² (assuming negligible air resistance).

First, we need to find the final velocity (v) at the end of the 3.5-second descent using the equation:

v = u + a * t

where:
- v is the final velocity
- u is the initial velocity (zero in this case)
- a is the acceleration due to gravity
- t is the time of descent

Since the initial velocity is zero, the equation simplifies to:

v = a * t

Plugging in the values:

v = 9.8 m/s² * 3.5 s
v ≈ 34.3 m/s

Now, we can calculate the average force using the equation:

F = m * a

Plugging in the values:

F = 103 kg * 9.8 m/s²
F ≈ 1009.4 Newtons

Therefore, the SWAT team member should apply an average force of approximately 1009.4 Newtons to the cable during the descent.

To find the average force that the SWAT team member should apply to the cable, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m × a.

First, let's find the acceleration. We can use the equation of motion:

s = ut + (1/2)at^2

where:
s = distance (27.5m)
u = initial velocity (0 m/s since the SWAT team member starts from rest)
t = time (3.5s)

By rearranging the equation, we get:

a = 2s / t^2

Now we can calculate the acceleration:

a = 2 × 27.5m / (3.5s)^2
= 2 × 27.5m / 12.25s^2
= 2.245 m/s^2 (rounded to three decimal places)

Now that we have the acceleration, we can calculate the force:

F = m × a
= 103kg × 2.245 m/s^2
= 231.235 N (rounded to three decimal places)

Therefore, the average force that the SWAT team member should apply to the cable is approximately 231.235 Newtons.