A diver springs upward from a dive platform that is 10.0 meters above the water. At the instant that she contacts the water her speed is 55.0 km/hr and her body makes an angle of 85.0° below the horizontal (i.e., 85.0° below the surface of the water). Determine her initial velocity vector, both magnitude and direction. Include a complete diagram of the situation.

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Problem 1: The baseball player A hits the baseball at VA = 40 ft/s and 0A = 60° from the horizontal. When the ball is directly overhead of player B he begins to run under it. Determine the constant speed at which B must run and the distance d in order to make the catch at the same elevation at which the ball was hit. A VA = 40 ft/s 15 ft B d C

A supply plane flies horizontally with a speed of 100 m/s and an altitude of 350 m. Use g = -10 m/s/s. A) What are the initial velocity components of an object that is dropped from the plane at the instant it is dropped? B) How fast is an object that is dropped from the plane traveling 7.5 seconds later?  C) What angle, below the horizontal, does the velocity vector of an object that is dropped from the plane make 7.5 seconds later?  D) How long does it take for an object that is dropped from the plane to hit the ground when air resistance is neglected?  E) How far does an object that is dropped from the plane travel in the horizontal direction?

Is this vector addition or subtraction? Then solve: An airplane flies with a velocity of 55.0m/s [35°N of W] with respect to the air (this is known as air speed). If the velocity of the airplane according to an observer on the ground is 40.0m/s [53°N of W], what was the wind velocity?

Goro Shigeno (Pitcher) and Joe Gibson Jr. (hitter) went head to head in the Major League Baseball (MLB) series. For the last pitch, Gibson hits the baseball with 82 ft/s at angle of 75°. When the ball is directly above Shigeno he begins to run under it. Determine the (a) the total distance that the pitcher runs and (b) the constant speed at which pitcher must run in order to make the catch at the same elevation at which the ball was hit. (Note: the distance between the pitcher and hitter is 70 ft.)

A boy decides to propose to his girlfriend in a hot air balloon. They are in the balloon, and it is moving 15 degrees south of east at a velocity 10 m/s relative to the air. When the balloon has a height of 90 m the boy is about to propose to but he drops the ring. The wind is also blowing to the east at 12 m/s relative to the ground. They now need to find the ring. a) What is the horizontal distance ( magnitude and direction) the ring lands on the ground from where it drops out of the balloon? b) What is the final velocity of the ring right before it hits the ground? c) Draw the vertical position vs time graph, velocity vs time graph, and acceleration vs time graph of the ring.

A student throws a water balloon at an initial angle θ = 23° above the horizontal with an initial speed v0 from a height h = 1.52 m. The target is located on the ground at a horizontal distance d = 7.5 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.  Determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

A fire hose ejects a stream of water at an angle of 36.1° above the horizontal. The water leaves the nozzle with a speed of 24.0 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire? Number i Units +

An aircraft has to fly between two cities, one of which is 600.0 km north of the other. The pilot starts from the southern city and encounters a steady 100.0 km/h wind that blows from the northeast. The plane has a cruising speed of 284.0 km/h in still air. In what direction (relative to east) must the pilot head her plane? Enter the angle in degrees where positive indicates north of east and negative indicates south of east How long does the flight take? h