The cork from a champagne bottle slips through the hands of a waiter opening it, moving with an initial velocity v0 = 15.6 m/s at an angle θ = 77.4° above horizontal. A diner is sitting a horizontal distance d away when this happens. Assume the cork leaves the waiter’s hands at the same vertical level as the diner and that the cork falls back to this vertical level when it reaches the diner. Use a Cartesian coordinate system with the origin at the cork's initial position.  Part (a)  Calculate the time, td in seconds, for the cork to reach the diner.   Part (b)  Reacting quickly to avoid being struck, the diner moves 2.00 m horizontally directly toward the waiter opening the champagne bottle. Determine the horizontal distance, d in meters, between the waiter and the diner at the time the cork reaches where the diner had previously been sitting.

Problem 9: An owl is carrying a mouse to the chicks in its nest. The owl is at that time is 4 m west and 10.5 m above the center of the 34 cm diameter nest, and flying east at 3.1 m/s at an angle 29° below the horizontal when it accidentally drops the mouse. Part (a) Calculate the horizontal position of the mouse when it has fallen 10.5 m, assuming the nest is at the origin of a coordinate system with east being positive. Numeric : A numeric value is expected and not an expression. x = Part (b) How far from the east edge of the nest did the mouse fall, in centimeters? Numeric : Anumeric value is expected and not an expression. d =

Recently a space x launch vehicle was coasting at a constant velocity of 15m/s in the + y direction relative to a space station . The pilot of the vehicle fired a special RCS thruster which causes it to accelerate at 8m/s^2 in the +x direction . After 9.1 s the pilot shuts off the RCS thruster . After RCS thruster is turned off find the magnitude of the vehicles velocity in +x direction.

A space vehicle is coasting at a constant velocity of 17.0 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.291 m/s2 in the +x direction. After 54.3 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction.

A projectile is launched with an initial velocity 38 m/s and an angle from the horizontal of 45°. The acceleration due to gravity is 9.81 m/s². Assume the projectile is launched from the surface of the Earth. i.e., at y (0) = 0. then the altitude of the projectile as a function of time is: y(t) = gt² + vo sin(0)t Where vo is the initial velocity. What is the maximum altitude achieved by the projectile?

A space vehicle is coasting at a constant velocity of 19.3 m/s in the +y direction relative to a space station. The pilot of the vehicle fires aRCS (reaction control system) thruster, which causes it to accelerate at 0.337 m/2 in the + direction. After 59.8 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction.

Consider a projectile launched with an initial velocity of 25.2m/s at an angle of θ0=30.9∘ above horizontal from level ground. After traveling a horizontal distance d=37.1m, it strikes a high cliff at a height hh above the original launch height. The impact angle, θ, may be above or below horizontal, depending upon whether or not the projectile has passed the apex of its flight. Use the Cartesian coordinate system provided in the drawing with the origin at the initial position of the projectile. Assume that air resistance is negligible.  Part (a)  How much time elapses, in seconds, from the moment the projectile is launched until it strikes the cliff?   Part (b)  At what height above the initial position, in meters, does the projectile strike the cliff?   Part (c)  What is the speed of the projectile, in meters per second, as it strikes the cliff?   Part (d)  What is the impact angle, in degrees measured counterclockwise from positive xxx, at which the projectile strikes the cliff?…

A skateboarder shoots off a ramp with a velocity of 7.9 m/s, directed at an angle of 51° above the horizontal. The end of the ramp is 1.4 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp? (a) Number_____  Units_____                                                            (b) Number ____  Units ____

For safety reasons, park rangers decide to start an avalanche on a mountain slope.  They fire an artillery shell at an angle of 520 above the horizontal with an initial speed of 295 m/s.  Thirty seconds later they see the explosion.  What is the x coordinates of the shell where it explodes, relative to the firing point?

A person stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of Vo = 22.0 m/s. The rock leaves his hand at a height of h = 46.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the rock leaves the hand. = i (a) What are the coordinates of the initial position of the rock? (Enter your answers in m.) хо Yo = Voy Vy y = 4o (b) What are the components of the initial velocity? (Enter your answers in m/s.) Vox m/s m/s 11 m m (c) Write the equations for the x- and y-components of the velocity of the rock with time. (Use the following as necessary: t. Assume that vx and v, are in m/s and t is in seconds. Do not include units in your answers.) oral m/s m/s Simuna wir + Accumo that y andy are in meters and it is in seconds. Do not