A fireworks show is choreographed to have two shells cross paths at a height of 117 feet and explode at an apex of 162 feet under normal weather conditions. If the shells have a launch angle e = 68° above the horizontal, determine the common launch speed vo for the shells, the separation distance d between the launch points A and B, and the time t from launch at which the shells explode. 45'

topic: Plane Curvilinear Motion

Q1) A team of engineering students designs a medium-size catapult which launches 8-lb steel spheres. The launch speed is v, = 80 ft/sec the launch angle is 0 = 35° above the horizontal, and the launch positionis 6 ft above ground level. The students use an athletic field with an adjoining slope topped by an 8-ft fence as shown. Determine: (a) the x-y coordinates of the point of first impact. (b) the time duration of the flight. (c) the maximum height h above the horizontal field attained by the ball. (d) the velocity (expressed as a vector) with which the projectile strikes the ground vo = 80 ft/sec fence 8' e = 35° 20 -100- 30

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Q 03: The track for this racing event was designed so that riders jump off the slope at 30°, from a height of 1 m. During a race it was observed that the rider shown in Fig. remained in mid air for 1.8 s. Determine the speed at which he was traveling off the ramp, the horizontal distance he travels before striking the ground, and the maximum height he attains. Neglect the size of the bike and rider. y C 30° h 1 m В R

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The tank is to be placed on a hill that is 1 km high above the ground. The enemy’s base is located at a horizontal distance of 10 km away and it is in a valley 0.5 km below the ground. Air resistance is neglected. Gravitational acceleration is constant and equal to 9.8?/?2 downwards. If the bomb is to be fired perfectly horizontally, what should the launching speed of the bomb be in order to hit the target? What is the duration it would take the bomb to hit the target? Find x(t) and y(t). Consider the initial location of the tank to be (0, 1 km)? Draw the trajectory of the bomb (x and y coordinates). Indicate clearly the value of x (horizontal displacement) when the bomb reaches the ground level. 5.     Draw the (?), ??(?), and ??(?) vertical above each other. Indicate key values on the graphs such as the start, the end, the maximum, the minimum and the x and y intercepts. PART 4 and 5 PLEASE.

A team of engineering students designs a medium-size catapult which launches 8-lb steel spheres.  The launch speed is vo = 80 ft/sec, the launch angle is ? = 35o above the horizontal, and the launch position is 6 ft above ground level.  The students use an athletic field with an adjoining slope topped by an 8-ft fence as shown. Determine: (a) the time duration tf of the flight. (b) the x-y coordinates of the point of first impact. (c) the maximum height h above the horizontal field attained by the ball. (d) the velocity (expressed as a vector) with which the projectile strikes the ground (or the fence).

A team of engineering students designs a medium-size catapult which launches 8-lb steel spheres.  The launch speed is vo = 80 ft/sec, the launch angle is ? = 35o above the horizontal, and the launch position is 6 ft above ground level.  The students use an athletic field with an adjoining slope topped by an 8-ft fence as shown. Determine: (a) the time duration tf of the flight. (b) the x-y coordinates of the point of first impact. (c) the maximum height h above the horizontal field attained by the ball. (d) the velocity (expressed as a vector) with which the projectile strikes the ground (or the fence).