Constants Part A (Figure 1)A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance di from A to C) is 200 m, the distance d2 (from C to B) is 150 m, and the speed vr of the current in the river is 5 km/hour. Suppose that the swimmer's velocity relative to the water makes an angle of θ-45 degrees with the line from A to C, as indicated in the figure To swim directly from A to B, what speed us, relative to the water, should the swimmer have? Express the swimmer's speed numerically, to three significant figures, in kilometers per hour. View Available Hint(s) Figure 1 of 1> km/hour Submit Provide Feedback v, 5 km/hour

In the Superbowl, a quarterback throws a football while standing at the very center of the field on the 50 yard line. The ball leaves his hand at a height of 5 ft and has initial velocity of ~v(0) =< 40, 35, 32 > ft/sec. Assume an acceleration of 32 ft/sec2 due to gravity, i.e., ~a(t) =< 0, 0, −32 >, and that the vector ~i points down fieldtoward the endzone and that the vector ~j points to the sideline. The field is 150 ft in width and 300 ft in length.(a) Determine the position function that gives the position of the ball t seconds after it isthrown.  (b) The ball is caught by a player 5 ft above the ground. Is the player in bounds or out ofbounds when he receives the ball? (Assume the player is standing vertically with bothtoes on the ground at the time of reception.)

the leprechaun in the shamrock patch was named O'Malley and since he was disrupted from sitting in his patch he decided to go off and play a round of his favorite sport in where leprechaun kick a gold coin from a tee into a post 317m away. if he kicked the coin at an angleof 60 degree at a velocity of 60 m/s how high was the arch of the rainbow created by the trajectory? how long did it take to get to the pot?

An airplane in a holding pattern flies at constant altitude alonga circular path of radius 3.50 km. If the airplane rounds half thecircle in 1.50 x 102 s, determine the magnitude of its (a) displacementand (b) average velocity during that time. (c) Whatis the airplane’s average speed during the same time interval?

An object is projected straight upwards with an initial velocity U. If T is the time taken to return to the point of projection, H is the maximum height and g is the acceleration due to gravity, derive how to solve for: (a.) time of flight, T, and (b.) the maximum height, H, that the projectile can achieve.

Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for t ≥ 0 arex = t − 2 sin t, y = 3 − 2 cos t Assuming that the plane flies in a room in which the floor is at y = 0, explain why the plane will not crashinto the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.] How high must the ceiling be to ensure that the plane does not touch or crash into it?

An eagle rises in a helical path given by the vector function r(t) =〈150cost, 150sint, 100t〉 where r is measured in feet and t is measured in minutes. Find the eagle’s velocity and acceleration vectors when it is directly above its starting position for the first time.

An astronaut on Mars kicks a soccer ball at an angle 45 ̊of with an initial velocity of 15 m/s. If theacceleration of gravity on Mars is 3.7 m/s2, (a) what is the range of the soccer kick on a flat surface? (b) What would be the range of the same kick on the Moon, where gravity is one sixth that of Earth?

the leprechaun in the shamrock patch was named O'Malley and since he was disrupted from sitting in his patch he decided to go off and play a round of his favorite sport in where leprechaun kick a gold coin from a tee into a post 317m away. if he kicked the coin at an angle of 60 degree at a velocity of 60 m/s how high was the arch of the rainbow created by the trajectory? how long did it take to get to the pot? the officials in dublin decided to add a goal post to "kick O coin" 300 meters away and so many 33 meters high. would O'Malley's kick have cleared this goal post?

The projectile at A is projected with an initial velocity v=23 m/s and an angle of projection theta degrees to hit target B. The following is required when theta+beta=90 and beta=6 degrees. a) Determine the distance R b) Determine the time of flight from A to B c) Determine the magnitude and the direction of the velocity at B e) Determine the maximum height the projection reached relative to point B f) if the object is given a constant horizontal acceleration in addition to its gravitational acceleration write down its horizontal equations of motions