Any physics experts out there...I need help with velocity questions?

Question

1. When a rifle is fired at a stationary distant target, the barrel is not lined up exactly with the target, why?

2. a physicist measures the acceleration of a falling body in an elevator accelerating at a constant 9.8m/s^2. What result does she obtain if the elevator is traveling (a) upward (b) downward

3.If an athelete can give himself the same initial speed regardless of the direction in which he jumps, how is his maximum vertical jump related to his maximum horizontal jump?

4.If an artificial earth satellite in an orbit around the earth's equator within a period of exactly one day, how does its motion look to an observer on the rotating earth if it orbits in the same direction as the earth turns?

5. An archer shoots an arrow from the top of a vertical cliff at an angle about the horizontal. When the arrow reaches the level ground at the bottom of the cliff, will it's speed depend on the angle at which it was shot?

Answer 1

5- Yes.....

1- Air resistance and wind play roll, so deviation in trajectory.

4- Looks still, not moving.

Not sure about 2 and 3.

Answer 2

1. gravity deflects the bullet downwards, so you aim above the target to compensate.

2. a. twice b zero

3. unclear what the question is

4. stationary

5. yes. If he shoots it mostly upwards, when it passes the edge of the cliff on the way back down, it will be moving fast relative to the ground, and that speed is carried through to the bottom of the cliff. Whereas if he shoots it horizontally, it's downwards speed will be the same as if he just dropped it down the cliff.

.

Answer 3

1.  When you fire an arrow from a bow, it is well known that    you have to aim higher than the target, otherwise the arrow will hit below the target.  This is because the arrow naturally falls under gravity, and you have to compensate for that.

    The same is true with a rifle,  you have to aim higher than the target

Because the bullet travels much faster than the arrow, you don't have to aim as high for the same target.

2.  (a)  upwards - 9.8   + 9.8   = 19.6 m/sec^2

    

                (b)  downwards - the falling body has the same   acceleration as the lift and will appear to be stationary relative to it.  The acceleration will appear to be zero.

3. (a) When jumping vertically, let his speed = "u"

                                    At the top, final speed  =  0

                                                   Acceleration   =   -g

                                                              Height   =   h

Applying equation of motion  ( v^2  =  u^2  +  2 * a * s  )

      The         0   =   u^2  +   2 * -g * h

  Height (h)    =       u ^2/ (2 * g)

(b) In a long jump, the maximum range is obtained by jumping at 45 degrees to the horizontal.

Formula for the range of a projectile is:

     Range  =        v^2 * sin ( 2 * angle) / g

Since angle  = 45 degrees  :          Range  =  v^2  * sin(90) / g

                                                          Sin (90)  =  1

                                                          Range  =  v^2/g

Comparing the two answers:-

      Height   =   u^2 / (2 * g)    and   Range   =   v^2 / g

Same initial speed,  so u =  v, and we can see that the range is double the height.

The horizontal jump is double the vertical jump.

                                          

4. The satellite will always appear to be in the same position in the sky.

   These  satellites are called "geostationary" satellites, and are use to receive and  transmit, e.g TV programs, telephone information,

etc. Since they appear to be stationary in the sky, the transmitting and receiving aerials don't have to move to track them.

5.  Ignoring air resistance.

Assuming that whatever angle the arrow is shot at, it will have the same Kinetic Energy  as it leaves  the bow.

( If it is aimed above the horizontal, it still has the same K.E.when it returns to  the level at which it left the bow.)

It then loses a fixed amount Gravitational Potential Energy as it falls, and therefore gains a fixed amount of Kinetic Energy whatever the angle.    It therefore reaches the bottom of the cliff always with the same  total K.E., and therefore always with the same  speed.

Answer 4

1)

It is aimed higher to compensate for the bullet falling toward the earth.

2)

Upward - double

Downward - zero

3)

The shorter he jumps in the horizontal direction, the higher he goes in the verticle direction.

4)

It will seem not to have moved at all.

5)

The higher the altitude the arrow reaches, the higher the speed at which it hits the ground.

Answer 5

1. Gravity pulls down projectiles.

2. (a) a = 2G  (b) a = 0G

3. Hor. jump much short if purely hor. and he plows into ground.

4. Geosynchronous.

5. Yes.