#3) A soccer ball is kicked in Ritter Park such that the initial velocity vector is at 56.0 degrees angle relative to the ground and the magnitude of the initial velocity vector is 30.0 m/s. What is the time of flight of the ball and how far did it go (neglect air resistance and assume the ground is infinitely flat)? Remember, equations first, algebra, numbers last. Report answer to three sig figs.

A boat moves so that its position vector, r metres, at time t seconds is given byr = 2t - i+ 2tj The unit vectors i and j are directed east and north respectively. (a) Find the time when the boat is due north of its initial position. ( seconds) (b) Find the time when the boat is travelling north. ( seconds) (c) Find the acceleration of the boat, state the direction of the acceleration. magnitude = ( m/s2), direction = (

(II) Three vectors are shown in Fig. 3–35. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the +x axis. y à (A = 44.0) 28.0° 56.0% FIGURE 3-35 Č (C = 31.0) Problems 9, 10, 11, 12, and 13. Vector magnitudes are given in arbitrary units. В (В %3 26.5)

A plane is heading on a bearing of 200° with an air speed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast. Determine, the resultant ground velocity of the plane.

(a) How far will a stone travel over level ground if it is thrown upward at an angle of 32.0o with respect to the horizontal and with a speed of 11.0 m/s. Assume the stone is launched at a height of 2.2m above the ground. (b) What is the maximum horizontal range that could be achieved with the same initial speed?

Q1 For the vectors in Fig. 3-32, with a = 4, b = 3, and c = 5, what are (a) the magnitude and (b) the direction of d × b,(c) the magnitude and (d) the di- y rection of à × 7, and (e) the magnitude and (f) the direction of b × c? (The z is not shown.) axis

I) (a) We will start with displacement, the straight line (as the crow or airplane flies distance) covered by a moving object starting from an initial location and arriving at a final location. Vector quantities will be written in bold face i.e. A. Consider the situation of an ant that travels east, i.e. along the x axis, for 8 cm then travels northeast, i.e. 45° from the x axis, for 11 cm. Represent each leg of this journey by a vector on your graph paper. Vectors are written as arrows with the direction going from the tail of the arrow to the head of the arrow and the length of the arrow proportional to the magnitude (size) of the vector. Indicate the first part of the journey by an arrow of length 8 cm whose tail starts at the origin of your graph and whose head is at 8 units along the positive x direction. Call this vector A which is the displacement of the first part of the ant's journey. Now starting at the head of A draw a vector B which represents the second part of the ant's…

*2-20. If o = 45°, F = 5 kN, and the resultant force is 6 kN directed along the positive y axis, determine the required magnitude of F, and its direction 6.

In 1939 or 1940, Emanuel Zacchini took his human-cannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net (see the figure). Assume that he is launched with a speed of 26 m/s and at an angle of 50°. (a) Treating him as a particle, calculate his clearance over the first wheel. (b) If he reached maximum height over the middle wheel, by how much did he clear it? (c) How far from the cannon should the net's center have been positioned (neglect air drag)?