Need help with projectiles

In summary, the problem involves a quarterback throwing a football to a stationary receiver 40.0m away at an initial angle of 37.0 degrees. The goal is to determine the initial speed of the ball, the time it takes for the ball to reach the receiver, and the ball's highest point during its flight. To solve this problem, we need to use the equations for vertical and horizontal motion, with v representing the original velocity. Substitution will need to be used to solve for v, and the time it takes for the ball to reach its maximum height and 40.0m can be expressed in terms of v and theta. Assistance is needed to solve this problem.
  • #1
Epif
6
0

Homework Statement


A quarterback throws the football to a stationary reciever who is 40.0m down the field. If the football is thrown at an initial angle of 37.0 degrees to the ground,
a. What is the initial speed of the ball?
b. How much time does it take for the ball to reach the reciever?
c. What is the ball's highest point during its flight.


Homework Equations


I took these images from wikipedia... Couldn't figure out that whole LaTeX thing.
122b1743350726387f11e0c0977d1abf.png

e48ae6cb0f47d2d9af591a41041cf925.png

4507e8151d7f4b9a5e7ea5ecc9599f56.png

ac74922e1ee9d3629919dbbeac1fcdff.png


The Attempt at a Solution


Well, I didn't get far. I figured you could break the ball's velocity into 2 parts, the vertical motion and horizontal motion, yielding vsin37 for vertical and vcos37 for horizontal motion. However, I don't know what value v is. I'm thinking that substitution will have to be used but I'm not sure where to go from here. I could really use some help! Thanks!
 
Physics news on Phys.org
  • #2
Suppose v is the original velocity... what is the time it takes the ball to get to its maximum height in terms of v and theta? what is the time it takes the ball to get to 40.0m in terms of v and theta?
 
  • #3


I understand your struggle with this problem. Projectile motion can be tricky, but with the right approach, we can find the answers to these questions.

First, let's define some variables:
- v = initial velocity of the ball
- θ = initial angle of the ball (37.0 degrees in this case)
- g = acceleration due to gravity (9.8 m/s^2)

a. To find the initial speed of the ball, we can use the horizontal and vertical components of the velocity. As you correctly stated, the vertical component is vsinθ and the horizontal component is vcosθ. Since the ball is thrown at an angle, we can use the Pythagorean theorem to find the total initial velocity:

v = √(vcosθ)^2 + (vsinθ)^2
v = √(v^2cos^2θ + v^2sin^2θ)
v = √v^2(cos^2θ + sin^2θ)
v = √v^2(1)
v = v

This may seem like we didn't get anywhere, but remember that we defined v as the initial velocity, so the initial speed of the ball is just v.

b. To find the time it takes for the ball to reach the receiver, we can use the equation for the vertical displacement of a projectile:

y = y0 + v0yt - 1/2gt^2

In this case, y = 40.0m (the distance the receiver is down the field), y0 = 0 (the initial height of the ball), v0y = vsinθ (the initial vertical component of the velocity), and g = -9.8 m/s^2 (since the ball is moving in the opposite direction of gravity). We can rearrange the equation to solve for time (t):

t = (v0y ± √(v0y^2 - 4(1/2)(-9.8)(40.0)) / 2(-9.8)
t = (v0y ± √(v0y^2 + 784)) / (-9.8)

Since we are only interested in the positive time (when the ball reaches the receiver), we can use the positive sign:

t = (v0y + √(v0y^2 + 784)) / (-9.
 

What is a projectile?

A projectile is any object that is launched or thrown into the air and moves along a curved path due to the force of gravity acting upon it. Examples of projectiles include bullets, arrows, and balls thrown during sports.

What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by its initial velocity, angle of launch, and the force of gravity. Other factors such as air resistance and wind may also play a role in altering the trajectory.

How is the range of a projectile calculated?

The range of a projectile is the horizontal distance it travels before hitting the ground. It can be calculated using the formula R = (V^2 sin2θ)/g, where R is the range, V is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

What is the difference between a projectile and a ballistic missile?

A projectile is any object that is launched into the air, while a ballistic missile is a specific type of projectile that is designed to be self-propelled and guided to a specific target. Ballistic missiles are typically used for military purposes.

How can projectiles be used in real life?

Projectiles have many practical applications in our daily lives, such as in sports, transportation, and military weaponry. They can also be used in scientific experiments and research to study the effects of gravity and motion.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
230
  • Introductory Physics Homework Help
2
Replies
38
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
4K
  • Introductory Physics Homework Help
Replies
19
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
18
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top