Projectile Motion Graph Analysis

In summary, the conversation discusses a golf ball being struck at ground level and its resulting speed as shown in a graph. The questions ask for the horizontal distance traveled before returning to ground level, the maximum height attained, and how to obtain the graph. The solution involves understanding projectile motion and using the horizontal velocity from the graph to calculate the distance traveled.
  • #1
robax25
238
3

Homework Statement



A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in Fig. 4-36, where t = 0 at the instant the ball is struck. The scaling on the vertical axis is set by ##v_a = 19~m/s## and ##v_b = 31~m/s##.

(a) How far does the golf ball travel horizontally before returning to ground level?
(b) What is the maximum height above ground level attained by the ball?
(c) How can I get the graph?

It is a projectile motion graph but I do not get any match with projectile motion graph.

Homework Equations


Horizantal Range= v²sin2θ/g
x=vt

The Attempt at a Solution


Horizontal distance
x= 19 *5=95m
 

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  • #2
Do not simply memorize formula without understanding the physics.

First, let's tackle part (a). Look at the graph. It is plotting the speed. It is maximum at the beginning and the end. Now, think, where will the golf ball has the LEAST speed? Where exactly in the trajectory does this occur? And what is the vertical component of the speed at this point? (you may want to sketch out the entire trajectory of the golf ball as a visual aid.)

Hint: this will give you the horizontal component of the velocity, and you MUST know that for a projectile motion, the horizontal component does not change (since there is no force in this direction to cause this velocity to change).

Once you have this horizontal velocity, you know the time of flight from the graph itself, finding the horizontal distance travel should be trivial.

Zz.
 
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Related to Projectile Motion Graph Analysis

1. What is a projectile graph problem?

A projectile graph problem is a type of physics problem that involves analyzing the motion of an object that is launched or thrown into the air. The resulting motion can be represented by a graph that shows the object's position, velocity, and acceleration over time.

2. How do you solve a projectile graph problem?

To solve a projectile graph problem, you first need to identify the initial conditions, such as the object's initial velocity and angle of launch. Then, you can use equations of motion and kinematic principles to calculate the object's position, velocity, and acceleration at different points in time. Finally, you can plot these values on a graph to visualize the object's trajectory.

3. What is the significance of the shape of a projectile graph?

The shape of a projectile graph can tell us a lot about the motion of the object. For example, a parabolic shape indicates that the object's motion is affected by gravity, while a linear shape suggests that the object is moving at a constant velocity. By analyzing the shape of the graph, we can determine how different factors, such as initial conditions and external forces, affect the motion of the object.

4. What are some real-life applications of projectile graph problems?

Projectile graph problems are used in many fields, including physics, engineering, and sports. They can help engineers design structures, such as bridges and buildings, by predicting the trajectory of objects that may impact them. In sports, projectile graph problems can be used to analyze the trajectory of a ball in different sports, such as baseball, basketball, and soccer.

5. What are some common mistakes to avoid when solving a projectile graph problem?

One common mistake is forgetting to convert units when using equations of motion. It is important to ensure that all units are consistent in order to get accurate results. Another mistake is neglecting air resistance, which can significantly affect the motion of an object. Additionally, it is important to pay attention to the direction of velocity and acceleration, as they can change throughout the motion of the object.

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