Ahorizontal rope is tied to a 50.0kg box on frictionless ice.
what is the tension in the rope if,
a. the box is at rest
b. the box moves at a steady 5.0m/s
c. the box has v_x=5.0m/s and a_x=5.0m/s^2

a) 0

b) 0

c) 250 N

Explanation:

A) When the box is at rest, it has zero acceleration, consequenly, the net force acting on the box is zero, and the rope has no tension. Tension = 0.

B) When the box is moving at a setady 5.0 m/s, again it has zero acceleration. So the same explanation above applies: net force = 0, and tension = 0.

C) When the box has Vx = 5.0 m/s and Ax = 5.0 m/s², you use the second law of Newton to find the net force:

F = mass × acceleration = 50 kg × 5 m/s² = 250 N

Since the box is on frictionless ice, there is not friction force, and the tension is equal to the net force. Tension = 250 N.

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min