5. Consider projectile motion with air resistance taken into account. If the resistance is proportional to the velocity, the initial velocity has vertical and horizontal components Voy and Vox, respectively, and the motion starts at the origin, show that the trajectory is given by y[x] V2 = _ V² In (1 _ _0x) + (Poy = ¹) x. gx - V == g Vox V Vox

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The velocity of a particle is given by v = 29t²-88t - 196, where v is in feet per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 4 seconds of motion. After you have the plots, answer the questions as a check on your work. -1 Questions: + 0 + 1 When t = 0.5 sec, V = 2 i When t = 3.3 sec, V = i + 3 +s, ft or m When the acceleration is zero, the velocity is i ft/sec, a = ft/sec, a = i i ft/sec. ft/sec² ft/sec²

At the Earth's surface, a projectile is launched straight up at a speed of 7.5 km/s. To what height will it rise? Ignore air resistance. 2.87e+06 Your response differs from the correct answer by more than 10%. Double check your calculations. m

1. A rock is thrown off a cliff at an angle of 51 with respect to the horizontal. The cliff is 126 m high. The initial speed of the rock is 24 m/s. (a) Fill in the following: Vo Vox Voy || || ✓ m S ES = ES m (b) VX (c) V (d) In your notebook, draw a sketch of the problem. Select the direction along the along the vertical axis (y-axis) that is positive (upwards or downwards). Select the direction along the along the horizontal axis (x-axis) that is positive (left or right). Select an origin. Draw the vectors for Vo, Vox Voy" V, Vx, Vy, ax, a¸. Label on your diagram the initial and final positions of the rock x, y, and xƒ‚ Yf. (e) How high above the edge of the cliff does the rock rise? Ay= m 00 (f) How far has it moved horizontally when it is at maximum altitude? Δx= m (g) How long after the release does it hit the ground? ground= (h) What is the range of the rock? Ax total ✔m S (i) What are the horizontal and vertical positions of the rock relative to the edge of the cliff at t = 4 s.…

The elevations of the ski jumping hill shown below are as follows: hA = 49 m hg = 3.5 m hc = 5.2 m If the velocity of a ski jumper is measured to be 25.4 m/s at position B, what will be the launch velocity (in m/s) at position C [round your final answer to one decimal place]? A hA C B hc nB

A rifle with a muzzle velocity of Vo shoots a bullet at a target R away at the level of the muzzle. How high above the target must the rifle be aimed so that the bullet will hit the target? (Neglect air resistance.) Let Vo = 250 m/s and R = 100 m. Find H

You are an engineer in charge of designing a new generation of elevators for a prospective upgrade to the Empire State Building. Before the state legislature votes on funding for the project, they would like you to prepare a report on the benefits of upgrading the elevators. One of the numbers that they have requested is the time it will take the elevator to go from the ground floor to the 102nd floor observatory. They are unlikely to approve the project unless the new elevators make the trip much faster than the old elevators. If state law mandates that elevators cannot accelerate more than 1.80 m/s2 or travel faster than 14.8 m/s, what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor? minimum travel time: