A playground is on the flat roof of a city school, 5.2 m above the street below (see figure). The vertical wall of the building is h = 6.70 m high, forming a 1.5-m-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of e = 53.0° above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (a) Find the speed at which the ball was launched. (Give your answer to two decimal places to reduce rounding errors in later parts.) m/s (b) Find the vertical distance by which the ball clears the wall. m (c) Find the horizontal distance from the wall to the point on the roof where the ball lands.

A dart is thrown at a dartboard 2.90 m away. When the dart is released at the same height as the center of the dartboard, it hits the center in 0.466 s. At what angle relative to the floor is the dart thrown? (Neglect any effects due to air resistance.) 0= Question Source: Freedman College Physics 3e | Publisher: Macmillan J 8 F12 Dil DD

In the Marvel comic series X-Men, Colossus would sometimes throw Wolverine toward an enemy in what was called a fastball special. Suppose Colossus throws Wolverine at an angle of 0 = 23.0° with respect to the ground (see figure below). Wolverine is d = 2.14 m above the ground when he is released, and he leaves Colossus's hands with a speed of v; = 22.6 m/s. d (a) Using conservation of energy and the components of the initial velocity, find the maximum height attained by Wolverine during the flight. m (b) Using conservation of energy, what is Wolverine's speed the instant before he hits the ground? m/s

Note: for this problem, you can neglect air resistance.An action hero is trying to use a circus cannon to get to the roof on a building 63.8 meters away. She launches herself from the ground with an initial velocity of 29.4 m/s at an angle 59 degrees above the horizontal, but instead of landing on the roof she hits the wall of the building. launching at a speed of 47.0 m/s. She goes over the building entirely and lands on the ground on the other side.How much time does she spend in the air? What is the height of the action hero at the peak of her trajectory? How far from her launch point will she land?

A golfer hits a shot to a green that is elevated 3.30 m above the point where the ball is struck. The ball leaves the club at a speed of 18.4 m/s at an angle of 45.0˚ above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands.

During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial speed v0 = 42 m/s at an angle θ = 43° above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem. a.)Express the magnitude of the ball’s initial horizontal velocity v0x in terms of v0 and θ.  b.)Express the magnitude of the ball’s initial vertical velocity v0y in terms of v0 and θ.  c.)Find the ball’s maximum vertical height hmax in meters above the ground.

During a baseball game, a baseball is struck, at ground level, by a batter. The ball leaves the baseball bat with an initial speed v0 = 41.7 m/s at an angle theta = 40.5 degrees above the horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Ignore air resistence throughout this problem. Enter an expression in terms of v0, theta, and g for the time it takes the ball to travel to its maximum veertical height.

Consider the frictionless water slide in the figure below. h₁ h₂ 1. If a 12.00kg dog starts from rest and slides down the water slide and has a velocity of 2.00 in the horizontal direction at point A, determine the height h₁ of the slide. m S m 2. If the bottom of the slide (point A) is 5.00m above the water level, how far horizontally does the dog travel between point A and when it reaches the water at point B? m оо B 3. How would increasing the mass of the dog impact your calculations above? It would result in the height of the slide being greater It would result in the height of the slide being less Equal Less than It would result in the dog's horizontal distance being greater It would result in the dog's horizontal distance being less It wouldn't impact any of the calculations 4. If the slide had friction, would the dog's velocity at point A be greater than, less than, or equal to the velocity without friction? Greater than

An industrious chipmunk creates an acorn catapult. This acorn catapult fires a 0.00543 kg acorn at an initial speed of 21.8 m/s. The catapult can be moved to any horizontal distance from the target and it can be set to shoot the acorn at any angle between 14° and 86.6°. The chipmunk will adjust the distance and angle until he gets a shot just right, and he deems a shot to be successful when the target is hit at the moment the acorn reaches its apex d) If the acorn hits the target and bounces back, losing 24.2% of its speed in the collision, what is the magnitude of the change in the acorn's momentum from immediately before the collision to immediately after the collision? e) If the duration of the collision described in part D is 3.01 x 10^-5 s, what is the magnitude of the average force the acorn imparts onto the target?

A boy is playing flying fox over a swimming pool as illustrated in the figure. A cable mounted on the top of a tall tower runs down to the ground with an angle = 26° with respect to the horizontal. The boy at the top of the tower grabs a pulley on the cable and slides down from rest. His initial height was ho 15 m above the water. When he reaches hi above the water, he releases his hands from the pulley and falls into the water. The boy is subject to the regular force of gravity (g-9.80665 m/s2). Ignore friction and air resistance. <=10m (a) Determine the speed of the boy at the moment he releases his hands from the pulley. Answer: 9.90 m/s (b) Determine the speed of the boy at the moment he splashes into the water. Answer: 17 (c) At what angle with respect to the horizontal does the boy enter the water? Answer: 57.85 degrees