A projectile fired at O follows a parabolic trajectory, given in parametric form by: x = 86t and y = 96t – 4.9t? where x and y are measured in meters and t in seconds. Determine: (a) ax and ay at any time t
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- 1110. In Fig. P-1109, a ball thrown down the incline strikes it at a distance s 254.5 It. If the ball rises to a maximum height h 64.4 ft above the point of release, compute its initial velocity vo and inclination 6. Ans. v. = 80.5 ft per see; 0= 53.1° FIG. P-1109 and P-1110.1つ7 3. An object undergoes motion in 2 dimensions under a constant acceleration of "-2.50 m/s at an angle of 50.0° with respect to the + x direction. It also has an initial velocity of vi = 7.00 m/s at an angle of 10,0° The object begins at the coordinates (0, 0). a) What are the coordinates of the object at t = 7.00 s? Want Cx, y) at t =?4 4tzテメ0チ=XT vse this Con Vxi = \V;l cos v +ハ Ay=lalsin Ga b) What is its total velocity vector of the object as a magnitude and direction at t = 7.00 s? a) Ov= Tonsin(20) where vo is the initial velocity in feet per second and is the angle of elevation. If yo 2300 feet per second and is changed from 13° to 14° use differentials to approximate the change in the range. Round your answer to the nearest integer. The range R of a projectile is R = Select one: Ⓒa. 2811 ft X b. 2593 ft C. 5623 ft d. 4568 ft 5186 ft e. = Incorrect 32
- b. Prove that, the range, R the time of flight, T and the Maximum height, H by a projectile are respectively given by; vỷ sin² e R = (5/g) sin20 , T = (2v,sin®), and H = 2gH.W: An object is thrown horizontally at 20m/s from a cliff top 45m above sea level. Find (a)the time to land; (b)the angle at which it hits the water; (c)the speed at which it hits the water. Ans. (a)3.03s (b)Ø = –54. 73 (c)35.79m/sA 50% Part (a) What is her velocity 2.7 s later in meters per second? sin() cos() tan() 9 cotan() asin() acos() 4. 6. atan() acotan() sinh() 1 2. 3. cosh() O Degrees O Radians tanh() cotanh() 0.
- A car P travels along a straight road with a constant speed v = 61 mi/hr. At the instant when the angle 0 = 68°, determine the values of i in ft/sec and 0 in deg/sec. Assume | = 119'. Answers: i ft/sec i deg/secThe figure shows the path taken by a drunk skunk over level ground, from initial point i ta final point f. The angles are 0, - 31.0, 0, - 46.0, and 0, - 84,0, and the distances ared, - 5.20 m, d, - 7.10 m, and dy - 12.0 m. What are the (a) magnitude and (b) angle of the skunk's displacerment fromi to f? Give the angle as a pusitive (cuunterckockwise) ur nugative (clotkwise) angle of magnitude less than 180', measured from the +xdlirection. (a) Number Units (b) Number UnilsProblem 1: т Your bow can fire arrows at 70÷. You shoot an arrow straight up into the air. After 1 second, you shoot another S arrow into the air. a) If you are shooting the arrows from 2 m above the ground, how far above the ground do the arrows collide? (Answer: 251 m) b) What are the velocities of the arrows when they collide? (Answer: ỦA c) On a single graph, plot y-position vs time for each arrow. This should show the intersection of where and when they collide. -4.9ŷ" vB = 4.99) т S
- An ion's position vector is initially r==(5i-6j+2k)m, and 10 s later it is r=(-2i+8j-2k)m.In unit-vector notation ,what is its Vavg during the 10s?The projectile is launched with a velocity vo. Determine the range R, the maximum height h attained, and the time of flight. Express the results in terms of the angle 0 and vo. The acceleration due to gravity is g. y R- Neglecting the size of the ball, determine the magnitude vA of the basketball's initial velocity and its velocity when it passes through the basket.A small aircraft for one person is used on a short horizontal flight. On its journey from A to B, lhe resultant velocity of the aireraft is 15 m s in a direction 60° east of north and the wind velocity is 7.5 ms due north. N 4 60 A Figure 1.20 Show that for the aircraft to travel from A to B it should be pointed a due east. b After flying 5 km from A to B. the aircraft returns along the same path from B to A with a resultant velocity of 13.5ms-. Assuming that the time spent at B is negligible, calculate the average speed for the complete journey from A to B and back to A. B.