B. Block on an incline A block of mass mı = 3.9 kg on a smooth inclined plane of angle 38° is connected by a cord over a small frictionless
pulley to a second block of mass m2 = 2.6 kg hanging vertically. Take the positive direction up the incline and use 9.81
m/s2 for g.
What is the tension in the cord to the nearest whole number?

Block on the incline:

• net force parallel to the incline

∑ F (para.) = m₁ g sin(38°) - T = m₁ a

where T is the magnitude of tension in the cord.

Notice that we take down-the-incline to be the positive direction, so that if the 3.9-kg block pulls the 2.6-kg block upwards, then the acceleration of the system is positive.

Suspended block:

• net vertical force

∑ F (vert.) = T - m₂ g = m₂ a

Solve both equations for the acceleration a, set the results equal to one another, and solve for T :

a = g sin(38°) - T/m₁

a = T/m₂ - g

==>   g sin(38°) - T/m₁ = T/m₂ - g

==>   T (1/m₂ + 1/m₁) = g (sin(38°) + 1)

==>   T = g (sin(38°) + 1) / (1/m₂ + 1/m₁)

==>   T = (9.81 m/s²) (sin(38°) + 1) / (1/(2.6 kg) + 1/(3.9 kg)) ≈ 25 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