At a picnic, there is a contest in which hoses are used to shoot water at a beac

Question

At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three different directions. As a result, three forces act on the ball, F1, F2, and F3. The magnitudes of F1 and F2 are F1=50.0N and F2=90.0N. F1 acts under the angle of 60degrees with respect to the x axis and F2 is directed along the x-axis. Find the magnitude and direction of F3 such that the resultant force acting on the ball is zero.

note: the diagram has the beach ball in the center of the origin. F2 is pointing towards the ball FROM due east along the x-axis. F1 is pointing towards the ball from the NW (in between the positive Y and -X axis), and F3 is pointing towards the ball from the SW (in between the -y and -x axis)

Explanation / Answer

find the vector for each force pointing towards origin.
F1 = (50cos60i - 50sin60j) = (25i - 43.3j)
F2 = (-90i + 0)

F1 + F2 + F3 = 0
F3 = -F1 - F2
F3 = -(25i - 43.3j) - (-90i + 0) = (65i + 43.3j)

magnitude of F3 = (652 + 43.32) = 78.1 N

direction = tan-1 (43.3/65) = 33.67 degree counter-clockwise from the negative x-axis

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.