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4 ‫اياد‬ (1) A ball is thrown vertically upwards from the ground, the ball is caught 2 s later by a person 10 m above the ground. What is the initial velocity of the ball? (2) A ball thrown horizontally from the top of the building 100 m high, the ball strikes the ground at 65 m horizontally from the bottom of the building. What is the speed of the ball just before it strikes the ground? (3) A car going around a curve of radius R at speed v experiences a centripetal acceleration ac if it goes around a curve of radius 3R at speed of 2v, what is the new acceleration? (4) A projectile was fired at 35o above the horizontal; at the highest point its speed was 200 m/s, what is the initial vertical component velocity? 

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(5) An object initially at the origin has a velocity v = 4i − 6 j 10    seconds later the object has a velocity of v `= 12i + 6 j find the average acceleration? (6) A particle moves at constant speed in a circular path with a radius of 2 cm. if the particle makes 4 revolutions each second, then what is the magnitude of acceleration? (7) A particle that is moving a long straight line deceleration uniformly from 40 m/s2 to 20 m/s2 in 0.5 s and then has a constant acceleration of 20 m/s2 during the next 4 s, calculate the average speed over the whole time interval?

3 ‫محمود‬ Questions 1- 3 are related to the following information:

Given the two vectors: A = 4i – 3k B = i + 2j + 2k Q1: The vector A – 3B is: (a) i + 6j -9k (b) i - 6j +9k (d) i - 6j -9k

(c) i + 6j + 9k

Q2: The angle between B and the positive z-axis is: (a) Cos-1 (-2/3) (b) Cos-1 (2/3) (c) Cos-1 (-3/2) -1 Cos (3/2) Q3: The vector C such that A – 4B + C = 0 is: (a) 8j - 11k (b) 8i + 5k (c) 8j + 11k + 8j + 5k

(d)

(d) 8i

5 ‫محمود‬ Example 5.22: A vertical rope is attached to an object that has a mass of 40.0 kg and is at rest. The tension in the rope needed to give the object an upward speed of 3.50 m/s in 0.700 s is: (a) 592 N

(b) 390 N

(c) 200 N

(d) 980 N

(e) 720 N

(Exercise 5.1) A block traveling on a rough horizontal surface with an initial speed of 40 m/s stops completely after traveling 160 m. find the coefficient of kinetic friction between the block and the surface? (Exercise 5.2) If an object travels at a constant speed of 30 m/s as it makes a horizontal circular turn of 200 m radius, what is the magnitude of the resultant force on the 80 kg object? (Exercise 5.4) A 10 kg crate is placed on a rough horizontal surface of µ k = 0.4 and connected with 12 kg hanging mass via a string that passes

over a massless and frictionless pulley as shown in the figure. What is the mass must be added to crate to make it move with constant velocity? 7 ‫محمود‬ Example 7.27: A block of mass m is pushed up against a spring, compressing it a distance x, and is the released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a second block of mass 4m, giving it a speed 3v. What distance was the spring compressed in the second case? a) x

(b) 2x

(c) 3x

(d) 4x

(e) 6x)

Example 7.28: A block of wood with a mass M = 4.65 kg is resting on a horizontal surface when a bullet with mass m = 18 g and moving with a speed of v = 725 m/s strikes it. The coefficient of friction between the block and the surface is μ = 0.35. The distance the block moves across the surface is: a) 1.1 m

(b) 3.3 m

(c) 0.41 m

(d) 11 m

(e) 15.1 m)

Exercise 7.2 For A = 3 i + j - k، B = - i + 2 j + 5 k، and C = 2 j – 3 k، find C· (A – B).