A rescue helicopter is lifting a man (weight = 797 N) from a capsized boat by means of a cable and harness. (a) What is the tension in the cable when the man is given an initial upward acceleration of 0.711 m/s2? (b) What is the tension during the remainder of the rescue when he is pulled upward at a constant velocity?

To answer this question, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

(a) To find the tension in the cable when the man is given an initial upward acceleration of 0.711 m/s², we first need to calculate the man's mass. We can do this by using the equation:

Weight = mass × acceleration due to gravity

Given:
Weight of the man = 797 N
Acceleration due to gravity = 9.8 m/s²

Using the formula, we can rearrange it to solve for the mass:

mass = weight / acceleration due to gravity

mass = 797 N / 9.8 m/s²

mass ≈ 81.33 kg

Now, we can find the tension in the cable. The tension in the cable is equal to the force required to lift the man, which is given by Newton's second law of motion:

Tension = mass × acceleration

Tension = 81.33 kg × 0.711 m/s²

Tension ≈ 57.86 N

Therefore, the tension in the cable when the man is given an initial upward acceleration of 0.711 m/s² is approximately 57.86 N.

(b) When the man is pulled upward at a constant velocity, the acceleration is zero. According to Newton's second law of motion, the net force on the man is also zero.

Since the weight of the man is acting downward, the tension in the cable must be equal to the weight of the man:

Tension = Weight

Tension = 797 N

Therefore, the tension in the cable during the remainder of the rescue when the man is pulled upward at a constant velocity is 797 N.