How Can I Solve These Vectors and Kinematics Exam Problems?

[sabah]

can someone please help me with these questionss... i have exam this week and i really need to know hwo to solve these problems. please... thank you and ya.. i do have the answers for it but i just can't get it when i try to solve it these problems are from my mid-term exam


(1) if B is added to A, the resultant has a x-component of 6 and a y-component of 1. if B is subtracted from A, the resultant vector has a x-component of -4 and a y component of 7. what is the magnitude of A?


(2) A ball is shot straight up from the surface of the Earth with an initial speed. neglect any effects due to air resistance, find the intial speed of the ball if the ball was in the air for 2 seconds?


(3) a crankshaft of radius 0.3m rotates at a speed of 1.2 m/s. though what angle does it travel in 1/2 minute.



(4) a bullet is fired with a horizontal velocity in the positive x direction from the top of an 80 m high cliff. the bullet strikes the ground 1330 m from the base of the cliff. find the initial speed of the bullet.


(5) a 5.0 kg object is suspended by a string whose mass is negligible from the ceiling of an evelator that is acceletaring downward at 2.6 m/s square. what is the tension in the string?


(6) a block is pushed up a frictionless 30 degree inclined by an applied force. if F=25 N and M=3.0 kg, what is the magnitude of the resulting acceleration of the block?

 

[malty]

can someone please help me with these questionss... i have exam this week and i really need to know hwo to solve these problems. please... thank you and ya.. i do have the answers for it but i just can't get it when i try to solve it these problems are from my mid-term exam


(1) if B is added to A, the resultant has a x-component of 6 and a y-component of 1. if B is subtracted from A, the resultant vector has a x-component of -4 and a y component of 7. what is the magnitude of A?


(2) A ball is shot straight up from the surface of the Earth with an initial speed. neglect any effects due to air resistance, find the intial speed of the ball if the ball was in the air for 2 seconds?


(3) a crankshaft of radius 0.3m rotates at a speed of 1.2 m/s. though what angle does it travel in 1/2 minute.



(4) a bullet is fired with a horizontal velocity in the positive x direction from the top of an 80 m high cliff. the bullet strikes the ground 1330 m from the base of the cliff. find the initial speed of the bullet.


(5) a 5.0 kg object is suspended by a string whose mass is negligible from the ceiling of an evelator that is acceletaring downward at 2.6 m/s square. what is the tension in the string?


(6) a block is pushed up a frictionless 30 degree inclined by an applied force. if F=25 N and M=3.0 kg, what is the magnitude of the resulting acceleration of the block?

Hi,

I'm sorry but we cannot help you until you show some of your attempts first. .

 

[ogb p]

(1) To solve this problem, we can use vector addition and subtraction. Let's say that A has components Ax and Ay and B has components Bx and By. We know that when B is added to A, the resultant vector has components 6 and 1, so we can set up the following equations:

Ax + Bx = 6
Ay + By = 1

Similarly, when B is subtracted from A, the resultant vector has components -4 and 7, so we can set up the following equations:

Ax - Bx = -4
Ay - By = 7

Now we have four equations and four unknowns, so we can solve for Ax, Ay, Bx, and By. Once we have those values, we can use the Pythagorean theorem to find the magnitude of A:

|A| = √(Ax^2 + Ay^2)

(2) To find the initial speed of the ball, we can use the kinematic equation:

y = y0 + v0t + 1/2at^2

Since the ball starts at the surface of the Earth, y0 = 0. We also know that the ball is in the air for 2 seconds, so t = 2. We can assume that the acceleration due to gravity is -9.8 m/s^2. Plugging in these values, we get:

0 = 0 + v0(2) + 1/2(-9.8)(2)^2
v0 = 19.6 m/s

(3) To find the angle traveled by the crankshaft, we can use the formula:

θ = ωt

Where ω is the angular velocity and t is the time. We are given the angular velocity (1.2 m/s) and the time (1/2 minute = 30 seconds), so we can plug those values in to get:

θ = (1.2 m/s)(30 s) = 36 radians

(4) To find the initial speed of the bullet, we can use the kinematic equation:

x = x0 + v0t + 1/2at^2

Since the bullet is fired horizontally, the initial vertical position (y0) and acceleration (a) are both 0. We also know that the final horizontal position (x) is 1330 m, the initial horizontal position (x