A ball is dropped from a height of 39.0 m.

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SUMMARY

A ball dropped from a height of 39.0 meters experiences a horizontal wind acceleration of 1.20 m/s². The analysis confirms that the ball's trajectory is a straight line due to the independence of vertical and horizontal motions. The relationship between vertical and horizontal displacement can be expressed in the linear equation y = mx + c, where 'm' represents the gradient. The time taken for the ball to reach the ground and its impact speed can be calculated using kinematic equations.

PREREQUISITES
  • Understanding of kinematic equations for projectile motion
  • Knowledge of vector decomposition in physics
  • Familiarity with linear equations and graphing
  • Basic principles of acceleration due to gravity
NEXT STEPS
  • Calculate the time of flight for the ball using the equation for free fall
  • Determine the final velocity of the ball upon impact using kinematic equations
  • Explore the concept of vector addition in projectile motion
  • Graph the trajectory of the ball to visualize the straight-line path
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Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators looking for practical examples of kinematic principles.

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Homework Statement


A ball is dropped from a height of 39.0m. The wind is blowing horizontally and imparts a constant acceleration of 1.20 m/s^2 to the ball.
a. Show that the path of the ball is a straight line and find the values of R and θ (R is the distance on the x-axis and θ is the angle between the point where the ball hits the ground and the x-axis)
b. How long does it take for the ball to reach the ground?
c. With what speed does the ball hit the ground?


Homework Equations





The Attempt at a Solution

 
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fsci13 said:

Homework Statement


A ball is dropped from a height of 39.0m. The wind is blowing horizontally and imparts a constant acceleration of 1.20 m/s^2 to the ball.
a. Show that the path of the ball is a straight line and find the values of R and θ (R is the distance on the x-axis and θ is the angle between the point where the ball hits the ground and the x-axis)
b. How long does it take for the ball to reach the ground?
c. With what speed does the ball hit the ground?


Homework Equations





The Attempt at a Solution


The acceleration due to the wind and the acceleration due to gravity are at rightangles to each other and thus vertical and horizontal motion can be analysed independently.

Graph this motion to get a picture.

The ball starts at (0,39)

Calculate how far vertically and horizontally the ball moves in 1 second - plot that point.

Repeat for 2 seconds.

Do those three points form a straight line?

That would be a place to start.
 
Prove that the relation of y and x is in form of a straight line.
y=mx+c

m is the gradient.
 

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