For a projectile lunched with an initial velocity of vo at an angle of e (between 0 and 90°), a) derive the general expression for maximum height hmax and the horizontal range R. b) For what value of e gives the highest maximum height?
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- Suppose you add two vectors A and B . What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?If three vectors sum up to zero, si1at geometric condition do they satisfy?
- You are on the roof of a Physics Building, 19 m above the ground. Your physics professor, who is 1.87 m tall, is approaching the building at constant speed of 2.28 m/s. If you wish to drop an egg on his head, how far should your professor be when you release the egg?Problem For a projectile lunched with an initial velocity of vo at an angle of 0 (between 0 and 90°), a) derive the general expression for maximum height hmax and the horizontal range R. b) For what value of e gives the highest maximum height? Solution The components of vo are expressed as follows: Vinitial-x = Vocos(0) Vinitial-y = Vosin(e) a) Let us first find the time it takes for the projectile to reach the maximum height. Using: Vfinal-y = Vinitial-y + ayt since the y-axis velocity of the projectile at the maximum height is Vfinal-y %3D Then, Vinitial-y + ayt Substituting the expression of vinitial-y and ay = -g, results to the following: t Thus, the time to reach the maximum height is tmax-height = We will use this time to the equation Yfinal - Yinitial = Vinitial-yt + (1/2)ayt if we use the time taken to reach the maximum height, therefore, the displacement will yield the maximum height, so hmax = Vinitial-yt + (1/2)ay? substituting, the vinitial-y expression above, results to…The figure shows the path taken by a drunk skunk over level ground, from initial point i to final pointL The angles are 6 - 30.0o: - 51.0 and - 77.0.and the distances are dy - 440 m d - 7.10m and dy - 13.0m What are the ta) magnitude and Ibi angle of the skunk's displacement fromi to Give the ande as a positive (counterdlockwisel or negative (clockwise) angle of magnitude less than 180 measured from the direction la) Number Units (b) Number Units
- A Canada goose flew 1.45 km [15.0 ̊ S of W] to feed, then it flew 1.64 km [70.0 ̊ S ofE] to its roosting location. Determine the goose’s displacement, using thegraphical/tip-to-tail method of vector addition. Answer to two significant digits.sin(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 32Question 4: A particle is thrown into air with initial speed vo making angle 0 with the horizontal as shown in Figure 1. The gravitational acceleration g and a constant acceleration a, due to a wind act on the particle. Find the range of the motion. a, 'w Figure 1 100
- a) What is the maximum height the projectile reaches? b) What is the total time up in the air? c) How far away did the projectile land? (Range) d) Where is the projectile at 10 seconds after firing?The exit velocity of a baseball (its velocity as it leaves the bat) is 128 feet per second, in the direction of 30 above horizontal and directly towards the monster 30 fcot tall center field wall. If the ball was hit 4 feet above ground level, find a) Parametric equations that model the trajectory of the baseball, b) The maximum height of the baseball's fiight, c) If the center field fence is 400 feet from home plate is this a home run? d) What is the impact velocity of the ball? =) Sketch a graph representing the trajectory of the ball.The world long jump record is 8.95 m (Mike Powell, USA,1991). Treated as a projectile, what is the maximum rangeobtainable by a person if he has a take-off speed of 9.5 m/s?State your assumptions