Electric field intensity at a point on the axial line of an electric dipals.

Two forces of magnitude 30 newtons \( (N) \) and 60 N act on an object at angles of \( 30^{\circ} \) and \( -45^{\circ} \) with the positive \( x \)-axis as shown in the figure. Find the direction and magnitude of the resultant force; that is, find \( F_{1}+F_{2} \). \( F_{1}+F_{2}=(\square) \mathbf{i}+(\square) \mathbf{j} \) (Simplify your answer, including any radicals. Use integers or fractions

A box sitting on a horizontal surface is attached to a second box sitting on an inclined ramp by a rope that passes over an ideal pulley. The rope exerts a tension force T on both weights along the direction of the rope, and the coefficient of friction between the surface and boxes is 0.4 . If the box on the right weighs 100 pounds and the angle of the ramp is \( 36^{\circ} \), how much must the box on the left weigh for the system to be in static equilibrium? The box on the left must weigh approximately (Do not round until the final answer. Then round to two decimal places as needed.)

A box sitting on a horizontal surface is attached to a second box sitting on an inclined ramp by a rope that passes over an ideal pulley. The rope exerts a tension force I on both weights along the direction of the rope, and the coefficient of friction between the surface and boxes is 0.6 . If the box on the right weighs 100 pounds and the angle of the ramp is \( 35^{\circ} \), how much must the box on the left weigh for the system to be in static equilibrium? The box on the left must weigh approximately \( \square \) pounds for the system to be in static equilibrium. (Do not round until the final answer. Then round to two decimal places as needed.)

Una esfea de Jan esta unifarmanate cargada con una densidad de carga de \( \frac{1.2 \times 10^{-5}}{\pi} \frac{\mathrm{c}}{\mathrm{m}^{3}} \). Calcular el modo del campo electrico a una distancia centro, en el interior \( (r<5) \) y en el exterior \( (r>5) \).

Item 21. Uma bola é largada do alto de um edificio e cai em direção ao solo. Sua altura \( h \) em relação ao solo, \( t \) segundos após o lançamento, é dada pela expressăo \( h=-20 t^{2}+ \) 3380. Após quantos segundos do lançamento, a bola atingirá o solo \( (h=0) \) ?