A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The hoist weighs 350 N. The ropes, fastened at different heights, make angles of 50° and 38° with the horizontal. Find the tension in each rope and the magnitude of each tension.

276 N and 225 N

Explanation:

Draw a free body diagram.  There are three forces on the hoist:

Weight force 350 N pulling down,

Tension force T₁ pulling up and left 50° from the horizontal,

Tension force T₂ pulling up and right 38° from the horizontal.

Sum of forces in the x direction:

∑F = ma

T₂ cos 38° − T₁ cos 50° = 0

T₂ cos 38° = T₁ cos 50°

T₂ = T₁ cos 50° / cos 38°

Sum of forces in the y direction:

∑F = ma

T₂ sin 38° + T₁ sin 50° − 350 = 0

T₂ sin 38° + T₁ sin 50° = 350

Substitute:

(T₁ cos 50° / cos 38°) sin 38° + T₁ sin 50° = 350

T₁ cos 50° tan 38° + T₁ sin 50° = 350

T₁ (cos 50° tan 38° + sin 50°) = 350

T₁ = 350 / (cos 50° tan 38° + sin 50°)

T₁ = 276 N

T₂ = T₁ cos 50° / cos 38°

T₂ = 225 N

v 154.9= 0.9 length length s little over 154.9cm

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.