. Prove that the trajectory of a projectile is parabolic, havingthe form y = ax + bx2. To obtain this expression, solve theequation x = v0xt for t and substitute it into the expressionfor y = v0yt – (1 / 2)gt2(These equations describe the xand y positions of a projectile that starts at the origin.) Youshould obtain an equation of the form y = ax + bx2 wherea and b are constants

. Prove that the trajectory of a projectile is parabolic, havingthe form y = ax + bx2. To obtain this expression, solve theequation x = v0xt for t and substitute it into the expressionfor y = v0yt – (1 / 2)gt2(These equations describe the xand y positions of a projectile that starts at the origin.) Youshould obtain an equation of the form y = ax + bx2 wherea and b are constants

Name: . Prove that the trajectory of a projectile is parabolic, havingthe fo
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Description: . Prove that the trajectory of a projectile is parabolic, havingthe form y = ax + bx2. To obtain this expression, solve theequation x = v0xt for t and substitute it into the expressionfor y = v0yt – (1 / 2)gt2(These equations describe the xand y posi

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 46P: A projectile is fired up an incline (incline angle ) with an initial speed vi at an angle i with...

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Prove that the trajectory of a projectile is parabolic, having the form y= ax + bx2. To obtain this expression, solve the equation x=voxt for t and substitute it into the expression for y=voyt- (1/2)gt^2. (These equations describe the x and y positions of a projectile that starts at the origin.) You should obtainan equation of the form y=ax+bx2 where a and b are constants.
Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for t ≥ 0 arex = t − 2 sin t, y = 3 − 2 cos t Assuming that the plane flies in a room in which the floor is at y = 0, explain why the plane will not crashinto the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.] How high must the ceiling be to ensure that the plane does not touch or crash into it?
An astronaut on Mars kicks a soccer ball at an angle 45 ̊of with an initial velocity of 15 m/s. If theacceleration of gravity on Mars is 3.7 m/s2, (a) what is the range of the soccer kick on a flat surface? (b) What would be the range of the same kick on the Moon, where gravity is one sixth that of Earth?
You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.5 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?
A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h, (a) in what direction must the pilot head her plane to move directly north across land and (b) how long does it take her to reach a point 300 km directly north of her starting point?
Check your Understanding A cyclist rides 3 km west and then tune around and tides 2 kin east. (a) What Is his displacement? (b) What is the distance traveled? (c) What is the magnitude of his displacement?
A projectile is fired up an incline (incline angle ) with an initial speed vi at an angle i with respect to the horizontal (i ) as shown in Figure P3.46. (a) Show that the projectile travels a distance d up the incline, where d=2vi2cosisin(i)gcos2 (b) For what value of i is d a maximum, and what is that maximum value?
MIT’s robot cheetah can jump over obstacles 46 cm high and has speed of 12.0 km/h. (a) If the robot launches itself at an angle of 60 at this speed, what is its maximum height? (b) What would the launch angle have to be to reach a height of 46 cm?
Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither 0 nor 90 : (a) Is the acceleration ever zero? (b) Is the vector v ever parallel or antiparallel to the vector a? (c) Is the vector v ever perpendicular to the vector a? If so, where is this located?
In the control tower at a regional airport, an air traffic controller monitors two aircraft as their positions change with respect to the control tower. One plane is a cargo carrier Boeing 747 and the other plane is a Douglas DC-3. The Boeing is at an altitude of 2500 m, climbing at 100 above the horizontal, and moving 30 north of west. The DC-3 is at an altitude of 3000 m, climbing at 50 above the horizontal, and cruising directly west. (a) Find the position vectors of the planes relative to the control tower. (b) What is the distance between the planes at the moment the air traffic controller makes a note about their positions?
In the Superbowl, a quarterback throws a football while standing at the very center of the field on the 50 yard line. The ball leaves his hand at a height of 5 ft and has initial velocity of ~v(0) =< 40, 35, 32 > ft/sec. Assume an acceleration of 32 ft/sec2 due to gravity, i.e., ~a(t) =< 0, 0, −32 >, and that the vector ~i points down fieldtoward the endzone and that the vector ~j points to the sideline. The field is 150 ft in width and 300 ft in length.(a) Determine the position function that gives the position of the ball t seconds after it isthrown. (b) The ball is caught by a player 5 ft above the ground. Is the player in bounds or out ofbounds when he receives the ball? (Assume the player is standing vertically with bothtoes on the ground at the time of reception.)
You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 3.6 ss for the dart to land back at the barrel.