Question

You throw a ball for your dog to fetch. The ball leaves your hand with a speed of 2 m/s, at an angle of 30◦ to the horizontal, and from a height of 1.5 m above the ground. The mass of the ball is 0.5 kg. Neglect air resistance in what follows.

(a) What is the acceleration of the ball while it is in flight? Report it as a vector, that is, specify magnitude and direction (or vertical and horizontal components; if the latter, specify which direc- tion(s) you take as positive).

(b) What is the kinetic energy of the ball as it leaves your hand?

(c) Consider the Earth as being in the system. What is the potential energy of the Earth-ball system (1) as the ball leaves your hand, (2) at its maximum height, and (3) as it finally hits the ground?

(d) How high does the ball rise above the ground?

(e) What is the kinetic energy of the ball as it hits the ground?

(f) Now let the system be the ball alone. How much work does the Earth do on the ball while it is in flight? (from start to finish)

(g) What is the velocity of the ball as it hits the ground? Report it as a vector.

(h) How far away from you (horizontally) does the ball land?

Answer 1

a) Acceleration of ball in flight is only in vertical direction, no horizontal component.

   ,  

Downward vectors are taken negative.

b)Kinetic energy of ball as it leaves hand

c) Potential energy of earth-ball system

1) as the ball leaves your hand

Ball reaches a maximum height of from initial position.

2) at maximum height

3) When it hits the ground,

d) From the ground the ball rises to a height of

e) Conserving energy ,

Kinetic energy of ball when it hits the ground is

f)Work done by earth on the ball while in flight is

g) When ball hits the ground,

Horizontal component of velocity

Vertical component of velocity

  

h) Using

  

Horizontal distance