A trebuchet was a hurling machine built to attack the walls of a castle under siege. A large stone could be hurled against a wall to break apart the wall. The machine was not placed near the wall because then arrows could reach it from the castle wall. Instead, it was positioned so that the stone hit the wall during the second half of its flight. Suppose a stone is launched with a speed of Vo = 25.0 m/s and at an angle of = 39.0°. What is the speed of the stone if it hits the wall (a) just as it reaches the top of its parabolic path and (b) when it has descended to half that height? (c) As a percentage, how much faster is it moving in part (b) than in part (a)?

In a jump serve in volleyball, the server throws the ball into the air and strikes it with his open hand from a position 9 m behind the net. An athletic player may be able to hit it when the bottom of the ball is 3 m above the ground. Without aerodynamic effects, a horizontally hit serve will never work—it will go into the net or go too far and out of bounds. How much time does it take for the ball to fall to the height of the top of the net (which is 2.41 m above the floor)? Also, calculate the minimum launch speed for the ball to make it over the net. Round the final answer to two decimal places. What is the range of the ball struck horizontally at this speed? Round the final answer to one decimal place. Do you think that putting topspin on the serve might improve the serve? The “sky serve” is intended to land on the opponent’s side at a nearly straight-down trajectory. If this serve were a sky serve, launched at the same speed, but at the nearly vertical angle of 85°, would it…

One of the tasks of the Mighty Hercules was to protect the town of Nemea from a lion.  One day Hercules sees the lion 320 feet away.  He strings his bow and lets an arrow fly.  The arrow leaves his bow travelling at 210 feet per second from a height of 6 feet.  He wants to hit the lion in the neck above the shoulders which is 4 feet off of the ground.   determine the launch angle that will hit the Lion. Find the right angle.

Before jumping from the bridge, Martin throws his water bottle to a friend standing on the bank of the lake. The bridge is 7.0 m high. The friend is standing on the bank 15.0 m from the base of the bridge with their hand 1.0m above the ground. What speed must Martin throw the bottle horizontally for it to reach his friend's hand?

A baseball with mass of 0.14 kg is batted into the air. It's initial speed is 38.1 m/s directed at an angle 26 degrees above the horizontal. Of the height of the ball when it was struck by the bat is 35 cm how high off the ground is the ball when it reaches the highest point in its trajectory?

A small rock is projected from the ground with the velocity with magnitude V0 and direction 53.1 degrees above the horizontal. A tall building is a horizontal distance of 26 m from where the rock was launched. The rock strikes the building 2 seconds after being launched. Neglect air resistance and assume the ground is level. At what vertical height above the ground does the rock the building?

A lacrosse player is practicing against a wall. The ball leaves his stick 2.3 meters above the ground at a 33.5 degree angle from the horizontal with a speed of 9.3 m/s. The ball then hits the wall, 3.7 meters away. How high above the ground does the ball make contact with the wall?

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1. Vivian is practicing her shooting accuracy with her slingshot by trying to shoot rubber balls into a bucket on the ground. For one particular shot for which the ball lands in the bucket, she fired her slingshot horizontally with an initial speed of 56.0 m/s at a height of 170 cm above the ground. (a) How far away is Vivian standing from the bucket? (b) What are the magnitude and direction of the ball's velocity when it lands in the bucket? Note: Please be mindful of significant figures. Also, you can assume that when the balls land in the bucket, they are on the ground.

Your little sister is running to the park in your neighborhood at a speed of 3.90 m/s when you suddenly realize she left her favorite playground ball behind. You throw her ball horizontally out the window of your apartment which is at a height of 45.0 m above the street and directly above the sidewalk. You throw the ball 8.00 seconds after she has passed below your window and she catches the ball! a) Ignoring air resistance, what is the initial speed that you must throw her ball so she can catch it just before it reaches the ground? b) How far down the sidewalk from the window is your sister when she catches her ball?