Incremental software development could be very effectively used for customers who do not have a clear idea about the systems nee
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Answer:
<em>Python code is as follows: </em>
********************************************************************************
#function to get number up to any number of decimal places
def toFixed(value, digits):
return "%.*f" % (digits, value)
print("Enter the price: ", end='', flush=True) #prompt for the input of price
price = float(input()) #taken input
totalCost = price + 0.05 * price #calculating cost
print("Total Cost after the sales tax of 5% is applied: " + toFixed(totalCost,2)) #print and output totalCost
************************************************************************************
Answer:
a) The y-component of velocity just before the ball hits the ground is -14.860 meters per second.
b) The ball is in the air during approximately 2.890 seconds.
c) The horizontal distance covered by the ball is 32.695 meters.
d) The magnitude of the velocity of the ball just before it hits the ground is approximately 18.676 meters per second.
e) The angle of the total velocity of the ball just before it hits the ground is approximately 52.717º below the horizontal.
Explanation:
a) The ball experiments a parabolic motion, which is a combination of horizontal motion at constant velocity and vertical motion at constant acceleration. First, we calculate the time taken by the ball to hit the ground:
(1)
Where:
,
- Initial and final vertical position, measured in meters.
- Initial speed, measured in meters per second.
- Launch angle, measured in sexagesimal degrees.
- Gravitational acceleration, measured in meters per square second.
- Time, measured in seconds.
If we know that ,
,
,
and
, then the time taken by the ball is:
(2)
This second order polynomial can be solved by Quadratic Formula:
and
Only the first root offers a solution that is physically reasonable. That is, .
The vertical velocity of the ball is calculated by this expression:
(3)
Where:
,
- Initial and final vertical velocity, measured in meters per second.
If we know that ,
,
and
, then the final vertical velocity is:
The y-component of velocity just before the ball hits the ground is -14.860 meters per second.
b) From a) we understand that ball is in the air during approximately 2.890 seconds.
c) The horizontal distance covered by the ball () is determined by the following expression:
(4)
If we know that ,
and
, then the distance covered by the ball is:
The horizontal distance covered by the ball is 32.695 meters.
d) The magnitude of the velocity of the ball just before hitting the ground (), measured in meters per second, is determined by the following Pythagorean identity:
(5)
If we know that ,
and
, then the magnitude of the velocity of the ball is:
.
The magnitude of the velocity of the ball just before it hits the ground is approximately 18.676 meters per second.
e) The angle of the total velocity of the ball just before it hits the ground is defined by the following trigonometric relationship:
If we know that ,
and
, the angle of the total velocity of the ball just before hitting the ground is:
The angle of the total velocity of the ball just before it hits the ground is approximately 52.717º below the horizontal.