Question 7 A projectile is fired with an initial speed of 64.9 m/s at an angle of 30.7 degrees above the horizontal on a long flat firing range. Determine the maximum height reached by the projectile. The maximum height is (Write the value and SI unit .)
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- Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what Initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2 .The same vectors that are shown in Figure P3.6 are shown in Figure P3.42. The magnitudes are F1 = 1.90f, F2 = f, and F3 = 1.4f, where f is a constant. a. Use the coordinate system shown in Figure P3.42 to find R=F1+F2+F3 in component form in terms of f. b. If Rx = 0.33, what is Ry? c. Check your result by comparing your answer to that of Problem 6. FIGURE P3.42Consider a projectile being launched with an initial speed of 49.5 m/s at a variety of initial angles. Refer to the figure. Part (a) What is the range, in meters, of the projectile if it is launched at an angle of θ1 = 70.6°? b. What is the range, in meters, of the projectile if it is launched at an angle of θ2 = 38°? c. What is the range, in meters, of the projectile if it is launched at an angle of θ3 = 90 − 70.6°, the complement of θ1?
- A person stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of v0 = 17.5 m/s. The rock leaves his hand at a height of h = 45.0 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. (a) What are the coordinates of the initial position of the rock? (Enter your answers in m.) x0= m y0= m (b) What are the components of the initial velocity? (Enter your answers in m/s.) v0x= m/s v0y= m/s (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 vy are in m/s and t is in seconds. Do not include units in your answers.) vx=17.5m/s vy=−9.8t m/s (d) Write the equations for the position of the rock with time, using the coordinates in the figure. (Use the following as necessary: t. Assume that x and y are…A person stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 15.0 m/s. The stone leaves his hand at a height of h = 52.0 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 stone leaves the hand. (a) What are the coordinates of the initial position of the stone? (Enter your answers in m.) (b) What are the components of the initial velocity? (Enter your answers in m/s.) (c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Assume that vx and vy are in m/s and t is in seconds. Do not include units in your answers.) (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Assume that x and y are in meters and t is in seconds. Do not include units in…It takes a golfer a total of three strokes to put the ball in the hole. The displacements of the three strokes are as follows: d1 = 4.20 m the north, d2 = 2.00 m northeast, and d3 = 1.10 m at ? = 35.0° west of south, as shown in the figure. If the golfer had made the hole in a single shot, what would be the displacement of the ball? (Assume the positive y- and x-axes are in the north and east directions, respectively. Give the magnitude of your answer in meters and the direction in degrees north of east.)
- A projectile is launched from a height H above the ground with speed V0 at an angle ao above the horizontal. In this problem, use a coordinate system where +y direction is upward. the+x direction is along the horizontal and to the right, and the x-coordinate of the projectile is initially zero. In this example, the maximum height reached by the projectile and the range of a projectile was calculated for a projectile launched from a height H above the ground and at an angle ao above the horizontal line. Calculate the time of flight, range, R, and maximum height, yMAX, reached by the projectile for the following special cases: a) Case 1: The projectile launched from the ground (H=0) b) Case 2: The projectile is launched horizontally (ao = 0)A stone is thrown horizontally from the highest point of a 95 m building and lands 115 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw. How long is the stone in the air in seconds? What must have been the initial horizontal component of the velocity, in meters per second? What is the vertical component of the velocity just before the stone hits the ground, in meters per second? What is the magnitude of the velocity of the stone just before it hits the ground, in meters per second?In the above drawing, a football is kicked from the ground with a velocity v at an angle θ andfollows the path indicated through the air. 2. The horizontal component of the velocity at the moment the ball is kicked isa. vb. v cos θc. v sin θd. zeroe. 9.8
- Find the ranges shown for the projectiles in the figure for an initial speed of 50 m/s at the given initial angles. Part A: What is the range, in meters, for the projectile with the angle of 15°? Part B: What is the range, in meters, for the projectile with the angle of 45°? Part C: What is the range, in meters, for the projectile with the angle of 75°?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.A quarterback passes a football from height h = 2.1 m above the field, with initial velocity v0 = 11.5 m/s at an angle θ = 31° above horizontal. Assume the ball encounters no air resistance, and use a Cartesian coordinate system with the origin located at the ball's initial position.a. create an expression for the football's horizontal velocity , vfx, when caught by a receiver in terms of v0, θ, g, and h.b. The receiver catches the football at the same height as released by the quarterback. Create an expression for the time, tf, the football is in the air in terms of v0, θ, g, and h. c. The receiver catches the ball at the same vertical height above the ground it was released. Calculate the horizontal distance, d in meters, between the receiver and the quarterback.