A dog tugs forward with force of 28n on a taut leash at an angle 30 above the horizontal what is magnitude component tension in leash?

$$T_x=Tcos\theta$$

$$=(28N)\cos30\degree$$

$$=(28N)(0.866)$$

$$T_x=24.208N$$

$$T_y=Tsin\theta$$

$$=(28N)\sin30\degree$$

$$=(28N)(0.5)$$

$$Ty=14N$$

The magnitude of tension in the leash is given

$$T=\sqrt{T^2_x+T^2_y}$$

$$=\sqrt{(24.208N)^2+(14N)^2}$$

$$T=\sqrt{581.6004N^2+196N^2}$$

$$T=\sqrt{777.6004N^2}$$

$$T=27.89N$$

$$\overrightarrow T=24.208\hat{i}+14\hat{j}$$