A student throws a water balloon with speed v ₀ from a height h = 1.98 mat an angle ? = 21? above the horizontal toward a target on the pound. The target is located a horizontal distanced d = 65 in from the student's feet. Assume that the balloon moves without air resistance. Use a Cartesian coordinate system with the origin at the balloon's initial position.

(a) What is the position vector, R _target , that originates from the balloon's original position and terminates at the target? Put this in terms of h and d, and represent it as a vector using i and j.

R _target = (v ₀ cos(?)t) i - (v ₀ sin(?)t - 0.5 gt ² ) j

(b) In terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. Your answer should no: include h.

r = (6.5/v ₀ sin(?))

(c) Create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, v ₀ , 8, and ?

(d) Determine the magnitude of the balloon's initial velocity v ₀ in meters per second by eliminating t from the previous two Impressions.

h Vo X d sin() cos() cotan() asin() tan() acos() JL ( 7 8 9 56 M4 Grade Summary Deductions Potential 97% Late Work % 100% Late Potential 97%