The horizontal distance that a projectile will travel in the air is given by the equation R = frac{v_0^2 sin(2 heta)}{g} where v_0 is the initial velocity of the projectile, heta is the angle of elevation, and g is the acceleration due to gravity (9.8 meters per seconds squared). Use the information to answer the following questions. (a) If you can throw a baseball with an initial speed of 33.3 meters per second, at what angle should you direct the throw so that the ball travels a distance of 107 meters before striking the ground? The solution set is { } degrees. (Type your answer in degrees. Use a comma to separate answers as needed. Do not round until the final answer. Then round to two decimal places as needed.)
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We are given that R = 107 meters, Vo = 33.3 m/s, and g = 9.8 m/s^2. We need to find the angle 0. So, we can rearrange the equation to solve for 0: 107 = (33.3)^2 * sin(2*0) / 9.8 Multiply both sides by 9.8: 107 * 9.8 = (33.3)^2 * sin(2*0) Simplify the right Show moreā¦
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A ball is thrown with an initial velocity of v0=20 m/s, with an angle of Īø=45Āŗ toward a wall, X=25 m, away. Below, make sure that you derive your answers first literally, and only then make your numerical applications. Take the coordinate system's origin, at the location the ball is thrown toward the wall. You can further take Earth's acceleration, g=10m/sĀ². a) What would be the range R of the ball, in terms of v0, g, and Īø, if there were no wall ahead? Express it further, in meters. b) What is the period of time T taken by the ball, to hit the wall, in terms of X and v0? Express T further in seconds. You can calculate the cosine of 45Āŗ recalling that cosĀ²Īø+ sinĀ²Īø=1, and cosĪø=sinĪø, for the given angle. c) Write the trajectory equation, y(t) as a function of of x(t). Accordingly calculate Y=y(T), in meters, at the time T, the ball hits the wall.
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Projectile flights in the following exercises are to be treated as ideal unless stated otherwise. All launch angles are assumed to be measured from the horizontal. All projectiles are assumed to be launched from the origin over a horizontal surface unless stated otherwise. For some exercises, a calculator may be helpful. Firing golf balls $\quad$ A spring gun at ground level fires a golf ball at an angle of $45^{\circ} .$ The ball lands $10 \mathrm{m}$ away. a. What was the ball's initial speed? b. For the same initial speed, find the two firing angles that make the range $6 \mathrm{m}$
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