Aman is pulling on a rope with a force of 63 n directed at an angle of 61◦ to the horizontal. what is the y-component of this force?

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Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m 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, rtarge t, 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. (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 not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

Ahot-air balloon takes off from the ground traveling vertically with a constant upward acceleration of magnitude g/4. after time interval δt, a crew member releases a ballast sandbag from the basket attached to the balloon. how many seconds does it take the sandbag to reach the ground? (express your answer in terms of δt)