A playground is located 3.5 m from the base of a cliff. This 3.5 m wide zone from the cliff's base is used by cheering spectators. A player at the top of the cliff launches a 4.50 N ball horizontally. What must be the minimum speed of the ball as it leaves the top of the cliff so that it misses the spectator area at the base of the cliff? The spectator area is 3.5 m wide and 12.0 m below the top of the cliff. 

You place a metallic sphere on a horizontal board. You accidentally hit the sphere, where it rolls off the board with a speed of 2.5 m/s. It hits the floor in 0.582 s. Calculate the height of the board measured above the floor. Ignore air resistance.

A missile is fired with a take-off speed of 120 m/s at an angle θ with respect to the ground. It experiences a horizontal acceleration of 50 m/s² along the x-axis in a direction opposite to the motion. Determine the value of θ so that the missile will cover the maximum distance.

Hint: use the following expression d/dθ(A•cosθ•sinθ - B•sin²θ) = A•cos(2θ) - B•sin(2θ)

During a film shoot, a stuntman has to jump off a moving car, which takes off from the cliff and crashes on the ground 30m away after 1.5 s. Determine the speed of the car as it takes off from the cliff. Assume there is no air resistance.

A motorcyclist is contemplating a leap from a cliff as shown in the figure below. The cliff stands 5.0 m above the water's surface, and the pool extends horizontally for 18 m. If the motorcyclist aims to clear the pool completely, what is the minimum horizontal velocity required for a successful jump?

An engineer is testing a new lightweight drone by launching it horizontally from a platform to see how far it can travel without propulsion. There's a fence 5.50 meters tall located 30.0 meters from the launch platform. The drone is launched from a height of 8.40 meters above the ground. What is the minimum horizontal speed required for the drone to clear the fence? Will it land safely in the designated area that starts 10.0 meters beyond the fence and extends for another 20.0 meters? Determine the total time the drone will be in the air from the moment of launch to when it lands.