A bullet is fired through a board 5.0 cm thick in such a way that the bullet's line of motion is perpendicular to the face of the board. The initial speed of the bullet is 450 m/s and it emerges from the other side of the board with a speed of 350 m/s. (a) Find the acceleration of the bullet as it passes through the board. (b) Find the total time the bullet is in contact with the board.

A spacecraft on its way to Mars has small rocket engines mounted on its hull; one on its left surface and one on its back surface. At a certain time, both engines turn on. The one on the left gives the spacecraft an acceleration component in the x direction of ax = 5.10 m/s², while the one on the back gives an acceleration component in the y direction of a = 7.30 m/s2. The engines turn off after firing for 670 s, at which point the spacecraft has velocity components of vx = 3515 m/s and vy = 4136 m/s. What was the magnitude and the direction of the spacecraft's initial velocity before the engines were turned on? Express the magnitude as m/s and the direction as an angle measured counterclockwise from the +x axis. magnitude direction m/s º counterclockwise from the +x-axis

A space vehicle starts at an initial velocity of 100 m/s along the positive x-axis, and accelerates into space. The acceleration is a(t)= (10m/s 3 )t 2 i + 2m/s 2 j The vehicle was at the origin at the time of the launch. Find the kinematic equations for the vehicle.  x(t)=  y(t)=

The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/s2 in a direction opposite to the train’s velocity, while the freight train continues with constant speed.  Take x = 0 at the location of the front of the passenger train when the engineer applies the brakes.  (a) If t = 0 is the instant when the engineer applies the brakes, at what later time will there be a collision?  (b) Where will the collision take place?  (c) On a single graph, sketch the position of the front of the passenger train and the back of the freight train.

A motorcycle starts at t = 0 from rest at x = 0 (the origin) and moves along a straight path (x-axis) with an acceleration of +2.8 m/s2. After travelling for 140 m, the rider slows down the motorcycle at 1.2 m/s2 (still going forward along the path) until its velocity is 16 m/s. At that point, he sees/hits a tree.(a)    Find the velocity and the time when the motorcycle reaches x = 140 m.(b)    How much time and how far does it take the rider to slow down the motorcycle from its velocity at x = 140 m to its final velocity of 16 m/s?(c)    Hence, find the distance between the origin and the tree.(d)    Sketch a well-labelled velocity-time graph from t = 0 to the time that the rider reaches the tree. Point out a relation between the graph and the answer in part (c)

A well-thrown ball is caught in a well-padded mitt. If the acceleration of the ball is 2.10 × 104 m/s2 , and 1.85 ms (1 ms = 10−3 s) elapses from the time the ball first touches the mitt until it stops, what is the initial velocity of the ball?

A Lockheed Martin F-35 Lightning II jet takes off from an aircraft carrier with a runway length of 107 m and a takeoff speed 77 m/s at the end of the runway. Jets are catapulted into airspace from the deck of an aircraft carrier with two sources of propulsion: the jet propulsion and the catapult. At the point of leaving the deck of the aircraft carrier, the F-35's acceleration decreases to a constant acceleration of 4.8 m/s2 at 23° with respect to the horizontal. (Assume that the F-35's initial direction along the deck of the aircraft carrier is the +x-direction and that the +y-direction is up.)   What is its velocity and speed at this time? (Enter your answers in m/s.) v(5.4 s)= (?î +?ĵ)   v(5.4 s)=   ? m/s How far (in m) has it traveled horizontally?

A bullet is fired through a board 10.0 cm thick in such a way that the bullet’s line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 4.00 × 102 m/s and it emerges from the other side of the board with a speed of 3.00 × 102 m/s, find (a) the acceleration of the bullet as it passes through the board and (b) the total time the bullet is in contact with the board.

A juggler throws balls straight up in the air. After the balls leave his hand and while it is in the air, explain WHY each of the following four statement is FALSE. Write the right answer. (a) The velocity of the ball is always in the same direction as it's acceleration. (b) The velocity of the ball is never in the same direction as it's acceleration. (c) The acceleration of the ball is zero. (d) The velocity of the pin is the same direction as it's acceleration on the way up.

Please answer all question parts: A Lockheed Martin F-35 Lightning II jet takes off from an aircraft carrier with a runway length of 97 m and a takeoff speed 72 m/s at the end of the runway. Jets are catapulted into airspace from the deck of an aircraft carrier with two sources of propulsion: the jet propulsion and the catapult. At the point of leaving the deck of the aircraft carrier, the F-35's acceleration decreases to a constant acceleration of 4.3 m/s2 at 33° with respect to the horizontal. (Assume that the F-35's initial direction along the deck of the aircraft carrier is the +x-direction and that the +y-direction is up.) (a) What is the initial acceleration (in m/s2) of the F-35 on the deck of the aircraft carrier to make it airborne? (Enter the magnitude.) (b) Write the position (in m) and velocity (in m/s) of the F-35 in unit vector notation from the point it leaves the deck of the aircraft carrier. (Use the following as necessary: t.) (c) At what altitude (in m) is…