Problem 1: In a time of 2.87 h, a bird ies a distance of 98 km in a direction 242 degrees east of north. Take north to be the positive y direction and east to be the positive x direction. Express your answers in krn/h. What is the x component of the bird's average velocity? What is the y component of the bird's average velocity? Problem 2: An airplane ies horizontale at a speed of 384 km/h and drops a crate that falls to the horizontal ground below. Neglect air resistance. If the altitude of the plane was 782 m, then how far, horizontally in meters, did the crate move as it fell to the ground? What was the speed of the crate, in m/s, just before it hit the ground? Problem 3: A soccer ball is kicked from the ground at an angle of 0 = 49 degrees with respect to the horizontal. The ball is in the air for a time t. = 1.7 s before it lands back on the ground. Numerically, what is the total horizontal distance, 4,, in meters, traveled by the ball in the time, 1.? Problem 4: A student standing on a cliff throws a stone from a vertical height of d=8.0md=8.0m above the level ground with velocity v0=24mlsv0=24mls at an angle 6=Z7n0=27o below the horizontal, as shown. It moves without air resistance. Use a Cartesian coordinate system with the origin at the initial position of the stone. With what speed, in meters per second, does the stone strike the ground? If the stone had been thrown from the clifftop with the same initial speed and the same angle, but above the horizontal, would its impact velocity be different? Problem 6: Find the ranges for the projectiles in the gure for the elevation angle of 0 = 38 5 and the initial speeds given in the data below. l-R1-i hRzd -R3-+ ll)tlwrxpt'rltaxunl 1) Find the range, in meters, for the projectile with a speed of 9.5 m/s. 2)Find the range, in meters, for the projectile with a speed of 19 m/s. 3) Find the range, in meters, for the projectile with a speed of 26 m/s. Problem 7: A car is traveling at constant speed of v = 20.3 m/s. Its tires have a diameter of d = 0.98 m. Randomized Variables v = 20.3 m/s d = 0.98 m Consider a point on the outer edge of the tire. What is the centripetal acceleration, a,, at this point in 111/52? If the car was traveling twice as fast, what would be the numerical value of the ratio of the new centripetal acceleration, an to the old centripetal acceleration? Problem 8: A runner taking part in the 200 In dash must run around the end of a track that has a circular arc with a radius of curvature of 35 In. Randomized Variables r=35m t=24.4s Ifhe completes the 200 m dash in 24.4 s and runs at constant speed throughout the race, What is his centripetal acceleration as he runs the curved portion of the track in III/s2