Edward

prove that derivative (y+3/2) = (e^x/2)....original question is diferenciate: x=ln(2y+3)

To find left part is easy, as well as inverse and derivate.

Thanks

a tennis ball of mass 0,06 kg hits vertically upwards with speed of 20m per second from the point 1.1 m above the ground. It reaches the height of 16 m.

1. Find the initial kinetic energy of the ball and its potential energy when it is at highest point

2. calculate its loss of mechanical energy due to air resistance

3. find the magnitude of the air resistance force on the ball assuming it to be constant while ball is moving.

4. with what speed does the ball land?

All previous attempt to answer were wrong!!! So, please do not copy those wrong answer !!!!!

a tennis ball of mass 0,06 kg hits vertically upwards with speed of 20m per second from the point 1.1 m above the ground. It reaches the height of 16 m.

With what speed does the ball land? 

The resultant of forces (vectors) P and Q is |P|. Resultant of forces 3P and 2Q (vectors), acting in the same direction has magnitude 2P. Find |Q|(vector) and angle between P and Q(vectors).

Two tugboats are towing a ship in a straight line Tug A is pulling with a force of 5000 N at 15 degrees above to the direction in which the ship is moving. Tug B with tension T is pulling at 25 degrees bellow to the direction in which the ship is moving.

a) Find T

b) as velocity is constant along the moving direction find the magnitude of drag force acting on the ship.

This is assumption in answering my questions.  I cannot understand how angle (pi/4) can be the same as tangent????? Or uy and u_y is not the same? Thanks

45 = arctan(u_y/u_x) or tan(u_y/u_x) = 1 --> uy/u_x = pi/4 (radians)

A particle moves with constant acceleration and its velocity at time t :

v= (5-0.1t)i +(3+0.2t)j

1. find a, u

2. find the time t when particle is travelling in direction NE and find its speed.

3. find the distance and bearing of the particle from the starting point at that time.

Find the set of possible value of rational function: 6x+6/x^2+3

The path of a bird flight is observed. The bird flies in vertical plane with a constant vertical acceleration of 8m/s^-2 downward. When observation begin, the bird is in flight at a height 3m. It rises to a maximum height and down again to finish on the tree at a height of 5m. The horizontal distance between its starting position and the tree is 18m. The bird takes 4 seconds to complete the flight.

1.Find the horizontal and vertical component of the initial velocity

2.Find the maximum height

r=(50-t+20 cos t) i +(200-5 sin t)j 

1. find maximum speed of object2. find the position of an object when acceleration is first perpendicular to the initial acceleration.

The position of vector of a particle relative to a fixed origin is denoted by vector r.

initially r= (20i+15j) and Vector v=3t²i+(1+t)j. Find the position of particle after

2 seconds: my result is r(2sec)=28i+19j, book says 32i+19j. Who is right?

Hi guys, I need some help/ equation: s=10+36t+3t²-2t³ (-4≤t≤4).Question: how many times the object goes through the origin?

My son ( A level/A*student) asked me for help: I suggested 3 way.

1) equation of degree 3 must have 3 real roots, so answer is 3 (as it is in book)

2) using graph seeing 3 real roots.

3) solve the equation and he will find 3 real roots again.

 But he was not happy with my help. He derivates the equation (got v) and at ds/dt=0, 

he found 2 turning points, add 1 and got 3 roots. He said that it is logical conclusion. I show  him graph, which showed different result, so he corrected, that turning points must be in the opposite sides of axis x. Now it worked. I studied  maths 4 years in Uni but I did not remember that rule: n turning points=n+1real roots, provided turning points are on different side of x axis. (Jason rules).

As it is my son's own deduction, is he right?

2 trains A and B start together from the rest, time of both 3 minutes, distance of both the same.

A: first 30 sec, a= 1m sec–², next 120 sec continues at that speed, last 30 sec decelerates uniformly:B : first 90 sec, a= 5/9 m sec–² , next 90 second uniform deceleration. What is the largest distance between trains?