a). (i) When two missiles are projected from the same point with samevelocity but in different directions, find the horizontal distance D, covered in each case, if t and t' are respectively the times of flight.(ii) Prove that the range, R, is 4√(hh'), if h and h' are the greatest heights in the two paths of the missile with a given velocity.

(i) (ii) (iii) A particle is projected horizontally from a point P, h metres above O, with a velocity of V metres per second. The only acceleration that the particle undergoes is the acceleration due to gravity (-g) vertically in a downward direction. There is no horizontal acceleration. h y P V S x Finds the displacement vector of the particle at time t. A package of supplies is dropped from a plane to a disabled sailboat (S) in the ocean. The plane is travelling at a constant velocity of 252 km/h and is 150 m above sea level and directly due west of the disabled sailboat. How long will it take the package to hit the water? (Take g = -10 m/s²) A current is causing the boat to drift at a speed of 1.8 km/h in the same direction as the plane is travelling. Between what two values (distances) can the plane drop the package so that it lands at most 40 m from the disabled sailboat?

(c) Neglecting air resistance, determine the firing angle for a bullet which fired with initial velocity of 150m/sec to hit a target located 400m above the level of gun point and at a horizontal distance of 2500m. Also specify the bullet velocity in vertical direction at the point of maximum height attained.

(II) A fire hose held near the ground shoots water at a speed of 6.5 m/s. At what angle(s) should the nozzle point in order that the water land 2.5 m away (Fig. 3–36)? Why are there two different angles? Sketch the two trajectories. FIGURE 3-36 Problem 23. 2.5 m–

(II) A baseball is hit with a speed of  27.0 m/s at an angle of 45.0°. It lands on the flat roof of a 13.0-m-tall nearby building. If the ball was hit when it was 1.0 m above the ground, what horizontal distance does it travel before it lands on the building?

y B (B=26.5) 56.0° A (A = 44.0) 28.0° C(C= 31.0) x 15. (II) For the vectors shown in Fig. 3-41, determine (a) B-2A, (b) 2A - 3B + 2C.

Raindrops make an angle 0 with the vertical when viewed through a moving train window (Fig. 3–52). If the speed of the train is vr, what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically? FIGURE 3-52 Problem 61.

An object moving in the xy plane with an acceleration vector given by a- (70)i (-90) m т 9.00 s2 and an initial velocity vector given by - (10") (20"); Vo m 13.00- m 22.0 %3D S Determine the velocity of the object when it reaches its maximum y-coordinate. Express your answer in unit vector notation.

(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 A (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. B (B = 26.5)