For a fixed initial speed, the range of a projectile is determined by the angle at which it is fired. For all but the maximum, there are two angles that give the same range. Considering factors that might affect the ability of an archer to hit a target, such as wind, explain why the smaller angle (closer to the horizontal) is preferable. When would it be necessary for the archer to use thelarger angle? Why does the punter in a football game use the higher trajectory?

Make a prediction regarding what launch angle will produce the maximum horizontal range for a projectile launched from level ground and landing back on level ground. Provide reasoning to support your hypothesis.

A projectile is fired with initial speed 150 m/s and an angle of elevation 45° from a position 10 m above ground level. Where does the projectile hit the ground and with what speed? Solution If we place the origin at ground level, then the initial position of the projectile is  (0, 10)  and so we need to adjust the parametric equations of the trajectory by adding 10 to the expression for y. With  v0 = 150 m/s,  ? = 45°, and g = 9.8 m/s2, we have x  =  150 cos    ? 4    t =          y  =  10 + 150 sin    ? 4    t −  1 2  (9.8)t2 =          . Impact occurs when y = 0, that is  4.9t2 − 75   2  t − 10 = 0.  Solving this quadratic equation (and using only the positive value of t), we get the following. (Round your answer to two decimal places.) t =  75   2  +    11,250 + 196 9.8  ≈   Then  x ≈ 75   2 (21.74) ≈    (rounded to the nearest whole number), so the projectile hits the ground about…

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Lesson: Projectiles If two projectiles have the same size and shape but one is heavier than the other, which will travel further horizontally if they are both launched at the same angle and speed? O The heavy one O They will both be the same O The light one O Not enough information to tell

Use a graphing utility to obtain the path of a projectile launched from the ground (h = 0) at the specified values of θ = 35°, v0 = 300 feet per second. In the exercise, use the graph to determine the maximum height and the time at which the projectile reaches its maximum height. Also use the graph to determine the range of the projectile and the time it hits the ground. Round all answers to the nearest tenth.

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3. Consider a ball undergoing a 2D projectile motion, whose position (unit: m) as a function of time (unit: s) is 3(t) = tî + (V3t – 5t²)ĵ, where t stands for time. (a) Find the initial launch angle of the projection. (b) Find the speed of the ball when it lands on the ground.

A golfer has a choice of hitting a ball at 51° or at 38°. For maximum distance, which should the golfer choose? Ignore air resistance

A soccer ball is kicked with an initial horizontal velocity of 18 m/s and an initial vertical velocity of 13 m/s. 1) What is the initial speed of the ball? 2) What is the initial angle ? of the ball with respect to the ground? 3) What is the maximum height the ball goes above the ground? 4) How far from where it was kicked will the ball land?