Hala+Al-Khalil

__ **Week 2 (Jan 30th 2012 )** __
 * 01. A certain cab has a total run of 190 m and a maximum speed of 305 m/min. It accelerates from rest and back to rest at 1.22 m/s². **
 * i). How far does the cab move while accelerating to the maximum speed starting from rest? **

305m/min = 5.08m/s ( by multiplying by 60 )

using the equation: v^2 = v.^2 + 2*a*x (5.08)^2 = 0 + 2*1.22*x > x=10.59m


 * ii). How long does it take to make the nonstop 190 m run, starting and ending at rest? **

Using the equation: v = v. + a*t (from rest to Max acceleration) : 5.08 = 0 + 1.22*t --> t = 4.163 Sec (from Max acceleration to rest) : 0 = 5.08 + 1.22*t --> t = 4.163 Sec SO t(total) = 4.163 + 4.163 = 8.327 Sec


 * 02. A stone is dropped into a river from a bridge 50 m above the water. Another stone is thrown vertically down 1.00 s after the first stone is dropped. The two stones st rike the water surface at the same time. **
 * i). How long does it take for the first stone to reach the water surface? **
 * i). How long does it take for the first stone to reach the water surface? **

Using the equation : y = v. * t + .5*a*t^2 50=.5*9.8*t^2 ---> t = 3.194 Sec
 * ii). What is the initial speed of the second stone? **

t1 = t2 +1 ---> t2 = 3.194-1 = 2.194 Sec Using the equation : y = v. * t + .5*a*t^2 50= v. * 2.194 + .5 * 9.8 * 2.194^2 -> v. = 12.03 m/Sec

__ **Week three (06th of February, 2012)** __

1. If **B** is added to **A** the result is 6.0 iˆ + 1.0 jˆ. If **B** is subtracted from **A**, the result is - 4.0 iˆ + 7.0 jˆ.

i. Find **A** and **B**

**A** + **B** = 6.0 iˆ + 1.0 jˆ **A** - **B =** -4.0 iˆ + 7.0 jˆ  **--->we sum-up the two equations and solve it for A and B**

**then we get -> A =**1.0 iˆ + 4.0 jˆ

**B =** 5.0 iˆ - 3.0 jˆ

ii. Find the magnitudes of **A** and **B** **A =** **(** 1.0^2 + 4.0^2 )^.5 = ( 17 )^.5 **B =**( 5.0^2 + 3.0^2 )^.5 = ( 34 )^.5

iii. What is the angle between **A** and **B**

**> we find the direction for A and B ( the angel for each )** **then we make a diagram and state both vector on it** **then we find the angel between the two vectors ( A and B )**
 * > the answer will be : the smallest angel = 106.92 Deg. --> the largest angel = 253.08 Deg. **


 * Professor's Note : Good job, work well done !**

__ **Week four (13 th February, 2012)** __ 1. A 0.5 kg rock is projected from the edge of the top of a building with an initial velocity of 10.5 m/s at an angle 54º above the horizontal. Due to gravity, the rock strikes the ground at a horizontal distance of 15.3 m from the base of the building. Assume: The ground is level and that the side of the building is vertical. The acceleration of gravity is 9.8 m/s². What is the height of the building?

**at the beginning we find V0x and V0y for V0 > V0x = 6.17175 m/s, V0y = 8.49468 m/s**

**( we should know that the value of velocity when the rock is coming back to ground will be equal to the value of the initial velocity, and that happen when the rock reaches the level of the top of the building when its falling to the ground )**

**first: we use the equation ( V2 = V1 + a*t ) to find the time required to reach the Max height, then we multiply that time by 2 to know how much time required for the ball to go back to the horizontal level of the top of the building** **Then .... (since V0x is constant all the time) we find using V0x the range of the ball at that time using the equation ( X = V0 * t )**

**we subtract this range from 15.3m, so we find this way the rage traveled by the ball afterwards.**

**second, we find the time from the point the rock gets back to the horizontal level of the top of the building till it reaches the ground, Using V0x and the equation (** **X = V0 * t )** **Using this time we can easily find the height of the building from the equation ( Y = V0 * t + .5 * a * t^2 ) and using the V0y ( which is the negative value of V0y in the first line of this answer )**

**Sorry For Being Late ,,,, I didn't know that you where going to post the answers today...**

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__**Week 05 ( 20th February, 2012)**__ A pelican flying along a horizontal path drops a fish from a height of 5.4 m. The fish travels 8.0 m horizontally before it hits the water below. The acceleration of gravity is 9.81 m/s2. a) What was the pelican’s initial speed? b) If the pelican was traveling at the same speed but was only 2.7 m above the water, how far would the fish travel horizontally before hitting the water below?

Professor's Note : Liked the new style ! Good job

__ **Week 06 ( no problem posted )** __

__ **Week 07 ( 05th of March, 2012)** __

01 . An object is hung from a spring balance attached to the celing of an elevator cab. The balance reads 65 N, when the cab is standing still. What is the reading when the cab is moving upward, (a) with a constant speed of 8 m/s and (b) with a speed 8 m/s while decelerating at a rate of 2.4 m/s²

First of all we should know that the spring balance measures the tension(T). in this case (the cap is moving upwards), T = mg + mf ,while f is the acceleration of the cab. (a) the speed is a constant ---> f = 0 ---> T = mg + 0 = mg = 65 N.   (b) f = -2.4 m/s ² ---> T = mg + (-2.4)m = 49 N

Professor's Note : Good job !

__ **Week 08 (March, 12th, 2012)** __

01. A crate is pulled by a force (parallel to the incline) up a rough incline. The crate has an initial speed of 1.5 m/s. The crate is pulled a distance of 7. 5 m on the incline by a 150 N force. The acceleration of gravity is 9 .8 m/s²

What is the change in kinetic energy of the crate? Mass of the crate is 15 kg. (Note: This is assigned as a HW problem too)

__ **Week 08 (March, 12th, 2012)** __

= **B** =

01. A loaded sled weighing 85 N rests on a plane inclined at an angle of 20⁰ with the horizontal. The coefficents of static and kinetic friction between the inclined plane and the sled are 0.25 and 0.15 respectively. a). What is the least magnitude of the force F, parallel to the plane, that will prevent the sled from slipping down the plane b). What is the minimum force required to start the sled moving upward? c). What value of F (force) is required to move the sled up the plane at constant velocity?


 * Week 9 (April 26th, 2012) **


 * 1) **A cord is used to vertically lower an initially stationary block of mass M at a constant downward acceleration of g/4. When the block has fallen a distance d,**
 * Draw a picture. **


 * A. Find the work done by the cord's force on the block **


 * B. Find the work done by the gravitational force on the block **
 * C. Find the kinetic energy of the block **


 * D. Find the speed of the block **




 * Week 10 (April 16th, 2012) **

01**. A steel ball of mass 0.5 kg is fastened to a cord that is 70 cm long and fixed at the far end. The ball is then released when the cord is horizontal. At the bottom of it's path the ball strikes, a 2.5 kg steel block initially at rest on a frictionless surface. The collision is elastic.**
 * Find, **
 * a) the speed of the ball **
 * b) the speed of the block, both just after the collision **


 * Hint: first draw a diagram. **
 * find the velocity of the ball, just before it hits the block. **

you haven't found the final answer ! I wish if you have explained the steps, reasoning why you are using each equations instead of giving the final answer

Please read the problem, we need to find the velocities after the collisions, not before and after

Note: you haven't used the fact that the collision is elastic

-- Professor**