Ball Acceleration and Trajectory Question

In summary: The x-component of the force is 9.8 m/s^2 and the y-component of the force is 1.2 m/s^2. I was a little confused by how to find R, though. According to the solutions guide, R=39.0m/tan(83°), but I'm not sure what equation they used for it. Can you help me out with that?
  • #1
hueyosie
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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 from the ball's starting point to the ending point and θ is the angle between the x-axis and the ball's landing point... sorry if that's not clear! It's in the book's diagram and I'm not sure how to get the image here)
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


I know that the x acceleration is 1.2 m/s^2 and the y acceleration is 9.8 m/s^2 (should gravity ever be a negative value?) but I'm not sure where to go from there. According to the solutions guide, θ=arctan(9.8/1.2)=83°, which I understand, but I'm not sure how to get the R value, (the solutions guide says R=39.0m/tan(83°) but I'm not sure what equation they used for it). Any help would be appreciated! I'm having trouble with questions with motion in two dimensions because I'm not sure how to approach the questions, so if anyone has any tips, I'd really appreciate that as well :)
 
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  • #2
Think of this question as a right triangle. If your bottom angle is 83°, assuming that you have found it already, then it is a simple matter of using the Pythagorean theorem to find R.
 
  • #3
tal444 said:
Think of this question as a right triangle. If your bottom angle is 83°, assuming that you have found it already, then it is a simple matter of using the Pythagorean theorem to find R.
Thank you so much! I understand that part now.
 

FAQ: Ball Acceleration and Trajectory Question

What factors affect the acceleration of a ball?

The acceleration of a ball is affected by several factors, including the force applied, the mass of the ball, and the friction between the ball and its surroundings. Other factors such as air resistance and gravity may also play a role.

How can the acceleration of a ball be calculated?

The acceleration of a ball can be calculated using the formula a = F/m, where a is acceleration, F is the net force applied to the ball, and m is the mass of the ball. This formula applies to situations where the ball is moving in a straight line. For situations where the ball is moving in a curved path, more complex equations may be needed.

What is the relationship between acceleration and velocity?

Acceleration and velocity are closely related concepts. Acceleration is the rate of change of velocity, meaning that an increase in acceleration will result in a greater change in velocity over time. In other words, a larger acceleration will cause a ball to speed up or slow down more quickly than a smaller acceleration.

How does the trajectory of a ball change with different accelerations?

The trajectory of a ball is affected by its acceleration. A higher acceleration will result in a steeper trajectory, while a lower acceleration will result in a flatter trajectory. Additionally, the direction of the acceleration will also impact the trajectory of the ball.

Can the trajectory of a ball be affected by external factors?

Yes, external factors such as air resistance, wind, and the surface the ball is rolling or bouncing on can all impact the trajectory of a ball. These factors can either increase or decrease the acceleration of a ball, resulting in changes to its trajectory.

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