4.7** 12. Suppose that the angle 0 in Figure 4.7 is 30° a) Find the components of the earth's gravitational acceleration along the initial veloc- ity vector (the x-axis in Figure 4.8) and perpendicular to the velocity vector (along the y-axis shown in the figure). b) If the initial muzzle velocity of the cannon is 600 m/s, how far in the x-direction, along the initial velocity, will the cannonball be after 2 seconds? y ө Figure 4.7 The projectile problem with an unusual choice of coordinate system. S#
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- Use the graph below to answer the next three questions. Two projectiles are launched on a planet without an atmosphere (g is NOT 9.8 m/s). Projectile A is in motion for 6 seconds, while projectile B is in motion for 3 seconds before hitting the ground. The +x direction is horizontal and the +y direction is up. 40 32 16 B. 2. 8. x (meters) 10 12 y (meters) 24A projectile is launched from ground level innitial speed of 202 an angle of ft/s of 60°. Find the following (using g = 32 ft/s²). at b) The maximum altitude attained (in feet). round your answer to 4 decimal places. a) Parametric equations of the projectile's trajectory. a symbolic function of t with No decimal numbers. Write x (t) and y(t) clearly so I can understand the steps, thanks. your answer should be c) The range of the с) round with an projectile (in feet). your answer to up decimal places. elevationQ:1 a)Take any two vectors A and B in three dimensional Cartesian coordinate system of your choice and prove the following statements: Dot product of vectors A and B is a scalar quantity Cross product of vectors A and B is a vector quantity Note: Choose same vectors for both statements. b) A ball is kicked at an angle of 35° with the ground. What should be the initial velocity of the ball so that it hits a target that is 30 meters away at a height of 1.8 meter? What is the time for the ball to reach the target?
- You throw a ball off a desk with a constant velocity of 5 m/s. If the desk is 2 meters above the ground, a) How far horizontally will the ball go before it hits the ground? b) Find the velocity in vector form the moment right before it hits the ground? What angle does the velocity make with the x-axis?On a dare from a friend, you decide to try to jump a canyon using your bicycle as shown in the figure below. We will define a successful jump as one that allows you to just make it to the edge of the canyon on the far side. Ꮎ Yramp Calculate all the following: A custom ramp has been constructed for you which is yo = 29.6 meters high and is tipped an an angle of 0 = 44.7 degrees. The canyon has a width of Xcanyon 106.8 meters. Xcanyon The initial velocity, vo, of your bike? meters/second The time spent flying through the air second guessing your judgement? secondsМon Gravity: on off O Gravity Force Velocity > Path U Grid Star Mass 0.5 Our Sun 1.5 2.0 Planet Mass 0.5 Earth 1.5 2.0 Fast 392 Earth Days Normal Clear Slow
- Please help with the solution to this problem using (km/s). I know we will use Hohmann Transfer and a combined plane change. In the opening scene of the movie “Gravity” Dr Ryan Stone (Sandra Bullock) and Matt Kowalsky (George Clooney) are required to transit from the Hubble Space Telescope (Altitude 600 km, 28.5 degree inclination) to the International Space Station (Altitude 400 km, 51.6 degree inclination) using nothing but their Manned Maneuvering Units (MMU). An MMU has a delta V capability of about 30 m/s, and it would be impossible to perform this maneuver with so little delta V, but… a.) How much delta V would be required for this maneuver? b.) What if the maneuver did not require an inclination change (altitude change only?)Choose the starting point of the soccer ball to be the origin (0, 0) of your reference frame, z axis pointing horizontal to the right, and y axis pointing vertical up. Y Part A Vo Write down the horizontal position of the soccer ball as functions of time t. Express your answer using variables vo. f., and physical constants as needed. z(t)= ΑΣΦHi, I tried so hard for this question but I couldn't succeed. Can you solve this question for me. The coordinates of the position of the rocket in the figure at the given moment are (4,4,2) km. Observers at A, B and C are trying to measure their position relative to the rocket. Calculate the directional cosines of the rAR rBR, rCR vectors measured by the observers at the given moment.
- magnitude gravitational force (between a planet with mass 9.00 * 10 ^ 24 and moon, with 2.40 * 10 ^ 22 average distance between their canters 2.10 * 10 ^ 8* m b) ? is the moon's acceleration in m/s^ 2 ) toward the planet(Enter the magnitude. ) m/s^ 2 the planets acceleration (in m/s^ 2 ) the moon?John is standing at point 0 at ground level facing east. He throws a ball at an angle of 60° (Eradians) at an initial velocity of 20 m/s. 1. Decompose the initial velocity Vo, in its x- and y-components (in simplest root form). Final answer: 2. Assume point 0 is the origin. Write down the vertical position function of the ball, ya(t), assuming that the gravitational acceleration is –9.8 m/s?, as well as the horizontal position function of the ball, xg(t), ignoring air/wind resistance (in simplest root form). Remember: s(t) =at² + vot + Sq, where vo is initial velocity and s, is initial position. Final answer: yB(t) = X¤(t) = 3. What is the maximum height of the ball? Final answer: 4. How long will it take for the ball to be back on the ground? Final answer:2. 3. 4. 5. 6. 7. Given two matrices, determine AB and BA. Is AB = BA? Floor KISWAY KYSUNYA A-134-431,8-13113| The position of a particle is given by r = where a is a constant. Find the velocity and sketch the trajectory. (Hint: In sketching the motion of a particle, it is usually helpful to look at limiting cases as t 0 and as t - 00.) The position of a particle at any time t is given by x = a, y = bt, where a and b are constants. Find the rectangular and polar components of its velocity and acceleration (a) at any time t, (b) when a = 12 cm, b = 1 cm/s², and when t = 3 s. A particle moves along a space curve C with a vector is given by r(t) = 3 cos cos 2t ê, + 3 sin sin 2t ê, + (8t - 4), a. Find a unit tangent vector T to the curve C. b. Show that p = pT A particle moves at a constant acceleration along the curve x₂ = x₁/100 from point A to point B. The velocity of the particle at A is 10 m/s, and 10 s later, at point B it is traveling at 50 m/s. Determine the total acceleration of…