COMPLETTE ALL THESE PHYSICS PROBLEMS.

YOU ARE REQUIRED TO SHOW ALL OF YOUR WORK, I ALSO WANT A CLEAR WRRITING. LASTLY, MAKE SURE THAT ALL YOUR ANSWERS ARE 100% CORRECT.

1. (10 Pts.) A projectile is right at the edge of a 50.0 meter-tall building (see gure below). It is then fired with an initial speed of 35.0 m/s at an angle 27 degrees above the horizontal and lands on the ground. Neglecting air resistance: (a) Show the parabolic path of the projectile. Show the initial velocity vector. Using the suggested coordinate system, what are xa and ya (initial x and y positions)? (b) Calculate the horizontal and vertical components of the initial velocity. (c) How long will the projectile be in the air until it lands on the ground? ((1) Where exactly does the projectile lands? (9) What is the maximum height the projectile reach to, measured from the ground? (f) At the landing, what is the speed of the projectile (impact speed)? (g) At the landing, what angle does the velocity vector make with the X-axis? Y 50m 2. (10 Pts.) A particle moves from point A (2m, - 3m, 4m) to point B (- 4m, 5m, 7m) in 4 seconds. (a) Write down initial and final position vectors r, and ry in terms of the unit vectors i, j, K. (b) Find the displacement vector in terms of the unit vectors. (c) Calculate the average velocity in terms of the unit vectors. (d) Calculate the average speed. 3. (5 Pts.) True or False: (Indicate for EACH statement below) A projectile is shot into the air from the ground and lands on the same level. Ignore the air resistance. ( ) The projectile's acceleration is constant throughout its flight. ) The projectile's acceleration is zero at the highest point in its trajectory. ) The projectile's speed is constant throughout its flight. ) The projectile's speed is highest at launch and landing. ( ) The projectile's speed is zero at the highest point in its trajectory. 4. (5 Pts.) A stone is thrown horizontally and follows the path XYZ down as shown. On the figure show the velocity vector of the stone at points X, Y, and Z. horizontal5. (10 Pts.) A river ows straight from East to West at a steady speed of 1.5 111/ s relative to the ground. A swimmer plans to swim across the river from point P on the southern bank, to point Q, exactly to the north of point P, on the northern bank. Swimmer's speed relative to the water flow is 3.2 m/ s. Obviously she needs to swim somewhat against the ow. (a) Draw a figure, showing all three relevant velocity vectors. Make sure you label these velocities with appropriate indices. (Swimmer, Water, Ground). (1)) Calculate the angle (relative to the water flow) at which the swimmer must swim. (c) Calculate the speed of the swimmer relative to the bottom of the river (the ground). Q 6. (5 Pts.) In each figure below the vectors for instantaneous velocity and acceleration for a moving particle are shown. Match each statement with a gure: (a) Slowing down and turning right. (meaning right of particle's path of motion!) (1)) Speeding up and turning left. (c) No change in speed and turning left. ((1) Slowing down and turning left. (9) Speeding up and turning right 1v s ./" 4:, ~1