Solve Ball Vector Problem: Distance, Vertical & Horizontal Components

In summary, the problem involves throwing a ball at a wall at a speed of 37.0 m/s and an angle of 43.0° above the horizontal. The wall is 20.0 m away from the release point. The horizontal and vertical components of the ball's velocity can be found using the equations V_x = V_0 cos(theta) and V_y = V_0 sin(theta) - gt. To find the distance above the release point where the ball hits the wall, you need to take into account the effects of gravity by solving for t using the horizontal distance and velocity.
  • #1
mossfan563
54
0

Homework Statement


You throw a ball toward a wall at speed 37.0 m/s and at angle θ0 = 43.0° above the horizontal (Fig. 4-35). The wall is distance d = 20.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its velocity as it hits the wall?

fig04_35.gif


Homework Equations


V_x = V_0 cos(theta)
V_y = V_0 sin(theta) - gt

The Attempt at a Solution



I was able to find b by using V_x = V_0 cos(theta) with theta being 43 degrees and V_0= 37.
When I tried to find part a, I thought it was a simple tan association.
tan (43) = x/20 -> x = 20*tan(43)
I got x = 18.65... and it was wrong.
I tried getting part c using V_y = V_0 sin(theta) - gt with:
V_0 = 37, theta = 43 and g = 9.8
Then I got stuck.
Am I doing it right? How do you approach a and c?
 
Physics news on Phys.org
  • #2
mossfan563 said:
When I tried to find part a, I thought it was a simple tan association.
tan (43) = x/20 -> x = 20*tan(43)
I got x = 18.65... and it was wrong.

That would work if the ball traveled in a straight line, at constant velocity. But that doesn't happen because of gravity.

I tried getting part c using V_y = V_0 sin(theta) - gt with:
V_0 = 37, theta = 43 and g = 9.8
Then I got stuck.
Am I doing it right? How do you approach a and c?

That's good, but you need to find t to finish the question.

Can you use the horizontal distance and velocity to find t?
 
  • #3


To solve this problem, we can use the equations for horizontal and vertical components of velocity, V_x = V_0 cos(theta) and V_y = V_0 sin(theta) - gt, where V_0 is the initial velocity, theta is the angle of release, and g is the acceleration due to gravity.

For part a, we need to find the horizontal distance traveled by the ball before hitting the wall, which is given by the equation x = V_x * t, where t is the time it takes for the ball to reach the wall. To find t, we can use the vertical component of velocity equation, V_y = V_0 sin(theta) - gt, and solve for t. This gives us t = (V_0 sin(theta))/g. Now, substituting this value of t in the equation x = V_x * t, we get x = V_0 cos(theta) * (V_0 sin(theta))/g. Plugging in the values given in the problem, we get x = 20.22 m. Therefore, the ball hits the wall at a horizontal distance of 20.22 m from the release point.

For part b, we can use the equation V_x = V_0 cos(theta) to find the horizontal component of velocity. Plugging in the values given in the problem, we get V_x = 31.28 m/s.

For part c, we can use the equation V_y = V_0 sin(theta) - gt to find the vertical component of velocity. Plugging in the values given in the problem, we get V_y = 14.27 m/s.

Therefore, the ball hits the wall at a horizontal distance of 20.22 m from the release point, with a horizontal velocity of 31.28 m/s and a vertical velocity of 14.27 m/s.
 

1. What is a ball vector problem and how is it solved?

A ball vector problem involves determining the distance, vertical and horizontal components of a ball's motion in a given scenario. This is typically solved using mathematical equations and principles such as the laws of motion and trigonometry.

2. How do you find the distance traveled by a ball in a vector problem?

The distance traveled by a ball in a vector problem can be found using the formula d = v*t, where d is the distance, v is the initial velocity of the ball, and t is the time it takes for the ball to travel that distance.

3. What are vertical and horizontal components in a ball vector problem?

Vertical and horizontal components refer to the vertical and horizontal motion of the ball, respectively. Vertical components are affected by gravity, while horizontal components are not. These components are used to calculate the overall trajectory of the ball.

4. How do you calculate the vertical and horizontal components of a ball's motion?

The vertical and horizontal components of a ball's motion can be calculated using the equations vy = v0y + at and vx = v0x, where vy and vx are the vertical and horizontal components, v0y and v0x are the initial velocities in each component, and a is the acceleration due to gravity.

5. What are some common mistakes made when solving ball vector problems?

Some common mistakes made when solving ball vector problems include neglecting air resistance, not converting units correctly, and not considering the effects of angles and inclines in the scenario. It is important to carefully read and understand the problem and double-check calculations to avoid these errors.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
549
  • Introductory Physics Homework Help
2
Replies
62
Views
4K
  • Introductory Physics Homework Help
2
Replies
53
Views
3K
  • Introductory Physics Homework Help
Replies
10
Views
863
  • Introductory Physics Homework Help
Replies
6
Views
537
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
776
  • Introductory Physics Homework Help
Replies
3
Views
696
  • Introductory Physics Homework Help
Replies
8
Views
1K
Back
Top