How Does Resistive Force Affect a Cricket Ball's Flight?

[physicshawk]

help !force vector problem

A cricket ball has weight 1.6 N. At any instant between being struck by the bat and reaching...?
the ground the ball is subject to a resistive force of constant magnitude 0.5 N. (I have solved the following part with inverted commas but I am mentioning it case it be of use to answer the next part of the question which I need to know about.)


“The diagram shows the directions in which the resistive force acts
i) immediately after the ball leaves the bat,

ii) at the highest point of the flight,

iii) immediately before the ball reaches the ground.

The resultant of the resistive force and the weight if the cricket ball is denoted by R. Find the magnitude and direction of R in each of the three cases.”

for the diagram see: http://www.flickr.com/photos/8625954...in/photostream

Assuming that the resistive force acts in a direction opposite to that in which the cricket ball is moving, state at which stage of the flight

a) the magnitude of the resultant is greatest

b) the angle between the resultant and the vertical is greatest.

I am able to vaguly work out part a but I don't know the approach to part b.

 

[Bill Nye Tho]

Your diagram isn't working.

 

[Basic_Physics]

R is the resultant of the weight of the ball and the resistive force. So you have a parallelogram with R being the diagonal. The vertical weight leg is downwards and a constant length. The other leg's direction and magnitude changes during the course of the parabolic trajectory.

 

[physicshawk]

sorry. will look into it and fix it as soon as possible.

 

[Nickie]

I would suggest approaching this problem by breaking it down into smaller parts and analyzing each part separately. First, let's look at the three different stages of the ball's flight and determine the magnitude and direction of the resultant force in each case.

i) Immediately after leaving the bat, the ball is moving upwards and the resistive force is acting downwards. This means that the resultant force is pointing in a direction between the two, and its magnitude will be less than the weight of the ball (1.6 N). To determine the exact magnitude and direction of the resultant, we can use vector addition. Since the two forces are acting in opposite directions, we can subtract the magnitude of the resistive force (0.5 N) from the weight (1.6 N) to get a resultant force of 1.1 N acting upwards at an angle of approximately 18.4 degrees from the horizontal.

ii) At the highest point of the flight, the ball is momentarily at rest and the resistive force is still acting downwards. This means that the resultant force is equal in magnitude to the resistive force (0.5 N) and is pointing downwards at an angle of 180 degrees from the horizontal.

iii) Immediately before reaching the ground, the ball is moving downwards and the resistive force is acting upwards. This means that the resultant force is pointing in a direction between the two, and its magnitude will be less than the weight of the ball (1.6 N). Using vector addition again, we can subtract the magnitude of the resistive force (0.5 N) from the weight (1.6 N) to get a resultant force of 1.1 N acting downwards at an angle of approximately 18.4 degrees from the horizontal.

Now, let's look at part a) of the question - at which stage of the flight is the magnitude of the resultant force greatest? From our calculations above, we can see that the magnitude of the resultant force is greatest at the highest point of the flight, where it is equal to the magnitude of the resistive force (0.5 N). This makes sense, as at this point the ball has stopped moving and is being pulled down by the resistive force.

For part b), we need to determine the angle between the resultant force and the vertical at each stage of the flight. At the highest point of the flight, the angle between the resultant force and the vertical is 180