At a local swimming pool, the diving board is elevated h = 8.5 m above the pool's surface and overhangs the pool edge by L = 2 m. A diver runs horizontally along the diving board with a speed of v0 = 4.2 m/s and then falls into the pool. Neglect air resistance. Use a coordinate system with the horizontal x-axis pointing in the direction of the diver’s initial motion, and the vertical y-axis pointing up.  Determine the horizontal distance, dw in meters, from the edge of the pool to where the diver enters the water.

As illustrated in the figure, consider a soccer player kicking a stationary ball of mass m = 0.5 kg. Assuming that the air resistance is negligible, the ball undergoes a projectile motion (shown in figure). It is recorded that the angle of release of the ball is 0 = 25.2° and the maximum height reached by the ball is h = 4.5 m. If the time during which the foot of the soccer player remained in contact with the ball is At = determine: (a) The speed of release, V, of the ball 0.12 s, (b) The horizontal distance, I, between the initial position of the ball and the landing point (c) The momentum, p, of the ball at the instant of takeoff (d) The magnitude of force, F, applied on the ball by the soccer player У

A small object is initially at rest at the top of a large solid sphere that is fixed on the ground. The small object then begins to slide along the surface of the large solid sphere, without friction. V₁ = 0 RI Part (a) Find the angle at which the small object loses contact with the large solid sphere. Part (b) Find the maximum horizontal distance traveled by the small object before it hits the ground. Take (xi, y₁) = (0,2R) as the coordinates for the top of the large solid sphere.

An extreme skier, starting from rest, coasts down a mountain that makes an angle of 35.3 ° with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.115. She coasts for a distance of 18.5 m before coming to the edge of a cliff. Without slowing down, she skis off the cliff and lands downhill at a point whose vertical distance is 4.32 m below the edge. How fast is she going just before she lands?