Consider a projectile launched form ground level at an angle of elevation with an initial velocity . The maximum horizontal range is given by xmax=(v 2/0 sin2θ)/g, where g is the acceleration due to gravity. Here is the problem: If a soccer ball is kicked from ground level with an initial velocity of 28 m/sec, what is the smallest positive angle at which the player should kick the ball to reach a teammate 48m down the field? Assume that the ball reaches the teammate at ground level on the fly. Round to the nearest tenth of a degree.

Chinook salmon can cover more distance in less time by periodically making jumps out of the water. Suppose a salmon swimming in still water jumps out of the water with velocity 6.03 m/s at 40.6° above the horizontal, re-enters the water a distance L upstream, and then swims the same distance L underwater in a straight, horizontal line with velocity 2.92 m/s before jumping out again. Where L=3.67 m; t1= 0.801 sec this is a time when fish are over the water; t2= 1.256 sec; Ttotal =2.057 sec; the average horizontal velocity is 3.57 m/s. Consider the interval of time necessary to travel 2L. How is this reduced by the combination of jumping and swimming compared with just swimming at the constant speed of 2.92 m/s? Express the reduction as a percentage.

A placekicker is about to kick a field goal. The ball is 21.7 m from the goalpost. The ball is kicked with an initial velocity of 19.1 m/s at an angle above the ground. Between what two angles, 0₁ and 02, will the ball clear the 2.67-m-high crossbar? Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identities may be useful: sec 0 = 1/(cos) and sec²0 = 1 + tan²0.) (a) Number (b) Number Units Units 0₂

A skateboarder shoots off a ramp with a velocity of 7.9 m/s, directed at an angle of 51° above the horizontal. The end of the ramp is 1.4 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp? (a) Number_____  Units_____                                                            (b) Number ____  Units ____