Lauren is going to ride in a hot air balloon While moored it

Lauren is going to ride in a hot air balloon! While moored, it is held from rising by two ropes attached to the base of the balloon\'s basket. The ropes are fastened at the other end to the ground on opposite sides of the balloon. One rope makes an angle of 30 degree with the ground and the other rope makes an angle of 40 degree with the ground. The net lifting force on the balloon is 5000 N. Draw and label a diagram to show this situation. Determine the tension in each of the ropes.

Solution

let tension in first rope=T1 let tension in second rope=T2 then equating the horizontal component, T1*cos(30)=T2*cos(40) so T1=0.884 *T2 then equating the vertical component, T1*sin(30)+T2*sin(40)=5000 putting T1=0.884 *T2 solving we get, T2=4609.19 N T1=4074.53 N