Aboy throws a stone horizontally from the top of a cliff of height h = 50.0 m towards the
ocean below. the stone strikes the water at a distance d = 60.0 m from the base of the cliff.

the time at which the stone lands in the water is 3.19s. calculate the initial speed of the stone?

An object resting on a table weighs 100 n. with what force is the object pushing on the table? with what force is the table pushing on the object? explain how you got your answer.

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.

What is the single most important equation in all of physics?