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ID: 2846205 • Letter: P

Question

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A projectile is launched at an angle of 45 degree to the horizontal from 6 ft above the ground at an initial speed of 100 ft/sec. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object. Answer parts a through d. Find the velocity and position vectors for t 0. The velocity vector is v(t) = The position vector is r(t) = Graph the trajectory. Choose the correct graph below. Determine the time of flight and range of the object. The projectile remains in the air for seconds. (Round to two decimal places as needed.) The projectile travels feet. (Round to two decimal places as needed.) Determine the maximum height of the object. The maximum height of the object is feet. (Round to two decimal places as needed.)

Explanation / Answer

a. Velocity vector = <70.71, 70.71 + a*t> ; where a is the accletation. It's value is -g initially but then changes to +g after t = 7.21


Position vector = <70.71t, 6 +70.71t + 0.25at^2> ; where a is the accletation. It's value is -g initially but then changes to +g after t = 7.21


b. A. is the correct graph


c. Time of flight = 14.51 seconds

Range of object = 1026 feet


d. Maximum height of object = 261.1 feet.