Ablock of mass m = 3 kg is held against a wall with a force f applied at an angle φ, as shown. there is a coefficient of static friction μs = 0.25 between the block and the wall. if φ = 60°, then the minimum f required to hold the block up is

29.7 N

Explanation:

At the minimum force F, the block will just begin to slide down, so friction force will be pointing up.

Sum of the forces in the x direction:

∑F = ma

N − F cos φ = 0

N = F cos φ

Sum of the forces in the y direction:

∑F = ma

Nμ + F sin φ − mg = 0

Substitute:

(F cos φ)μ + F sin φ − mg = 0

F (μ cos φ + sin φ) = mg

F = mg / (μ cos φ + sin φ)

Given m = 3 kg, μ = 0.25, and φ = 60°:

F = (3)(9.81) / (0.25 cos 60° + sin 60°)

F ≈ 29.7 N

a. is the answer because they are not shared

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