A football is kicked from a cliff with a takeoff speed of 30 m/s and a launch angle of 35°. Calculate the angle of the ball after it has covered a horizontal distance of 75 m.

A gardener is watering his plants on sloppy land inclined at 20° as shown in the figure below. The water is leaving the pipe at an angle of θ° with respect to the slope. Determine the angle at which the water should leave the pipe so that it covers the maximum distance 'd'.

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

A pitcher releases a baseball horizontally at a velocity of 15 m/s from a height of 1.5 m. The batter is positioned 20 m away. Neglecting air resistance, determine the vertical distance the ball will drop by the time it reaches the batter.

Rocks on a slippery mountain can turn into swift projectiles as they slide. Imagine a rock at the ridge of a mountain incline at a 22° angle below the horizontal, with an initial velocity of 6.0 m/s. If the mountain's edge is 13 m above the ground, calculate the horizontal distance between the base of the mountain to the point at which the rock hits the ground.

A thief steals some precious diamonds preserved as ancient treasures in a museum. The security comes to know about the robbery and they carry out a search operation for the stolen diamonds. The thief finds himself locked inside as all the entrances and exits are sealed. In order to save himself from getting caught along with the diamonds he has to throw the diamond pouch to his partner who is outside the gate as shown in the figure. Determine the angle at which the pouch needs to be thrown so that it safely reaches the partner thief.

A golfer hits a golf ball with an initial velocity of 40 m/s aiming directly at a flagstick positioned 150 m away on the same level of the course. At what angle should the golfer aim their shot to ensure it reaches the flagstick?

Twenty magic balls each weighing a quarter of a kilogram are contained in a thin bag of negligible weight. This bag of magic balls is carried by a 90-kg floating genie descending with a constant downward velocity of 8 m/s. One of the magic balls is thrown from the bag initially at 6 m/s perpendicularly to the downward path of the genie. This is measured relative to a stationary speed meter in the bag. After 12 s, the genie sees the thrown magic ball bounce for the first time. Calculate how far the genie was from the ground when the magic ball was thrown. Assume that the genie continues his descent at a constant speed of 8 m/s and he can be treated like a point-like object.

A rescue helicopter is flying horizontally at a height of 150 m above sea level to deliver emergency medical supplies to a boat in distress near the coast. The helicopter is traveling at a speed of 100 km/h parallel to the coastline. Neglecting air resistance, calculate the distance from the boat at which the supplies should be dropped to ensure they land accurately in the water close to the boat, taking into account the height from which they are dropped.

Plants depend on the explosive mechanism for seed dispersal. A pod opens up explosively on a level ground firing a seed with an initial velocity of 55 m/s at 54.0° above the horizontal. Assuming negligible air resistance, find the seed's horizontal and vertical components of acceleration and velocity at the highest point in its trajectory.

You play a game with your friends, for which you are to throw a disc on the top of a rocky mound from a certain distance. During your turn, the disc is launched upward at an angle of 35° to the horizontal and lands on the top edge of a rocky mound that is 36 m away. The launching speed of the ball is 24.0 m/s. Ignoring air resistance, find the height of the rocky mound.

A water balloon is released from a stationary hot air balloon that is 100 meters above the ground as shown below. The water balloon is released with an initial velocity of 15.0 m/s at an angle of 30.0° from the horizontal. Calculate the magnitude of the velocity of the water balloon at the instant it lands.