Aplank 2.65 m long is supported by a cable, and a small ledge. the cable attaches 79.7 cm from the ledge, and makes an angle of 40.3 with the plank. it can hold 2648 n. how close (in meters) to the end of the plank can a 76.4 kg person walk before the cable breaks? ignore the mass of the plank itself.

0.51 m

Explanation:

Given :

Plank length = 2.65 m

Distance from the ledge from which the cable is attached = 79.7 cm = 0.797 m

Angle = 40.3 degree

Mass of the man, m = 76.4 kg

Now the net torque acting on the plank is zero.

Therefore, maximum torque applied by cable is

    = 2648 x 0.797 x cos (40.3)

    = 1609.5 N-m

We know that the man should apply the same torque,

Therefore, x 76.4 g = 1609.5

                  x =2.14 m

Therefore, length to the end of the plank is = 2.65-2.14

                                                                         =0.51 m

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50