Projectiles: Launch speed and horizontal distance

In summary, the problem involves finding the launch velocity and horizontal range of a projectile shot at 45 degrees. The launch velocity is calculated using the formula V = - 1/2gt, where g is the acceleration due to gravity and t is the flight time. The horizontal range can be calculated by finding the vertical and horizontal components of the launch speed using sin45 and cos45, respectively. Then, using the flight time and horizontal component, the range can be calculated. A formula can also be derived from first principles to find the horizontal range using the launch velocity.
  • #1
gratsoy
2
0
New to the forums, just starting a physics 11 course online and having some troubles with formulas.

Homework Statement



Projectile shot straight upwards, flight time = 4.70 sec
Second Launch at 45 degrees (horizontal range approx. 50-60 meters

A) Find Launch Velocity
B) Find Horizontal Range when shot at 45 degrees

Homework Equations



d = vit +1/2gt2

V = - 1/2gt ("made" this one myself from above formula, unsure if correct)


The Attempt at a Solution




Launch velocity

V = - 1/2gt
g = -9.8m/s
t = 4.7s

V = -[((1/2(-9.8))(4.7)]
V = -((-4.9)(4.7))
V = 23.0 m/s


I have no idea how to calculate the horizontal range, I need a formula that incorperates the 45 degrees

Thanks in advance!
 
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  • #2
gratsoy said:
New to the forums, just starting a physics 11 course online and having some troubles with formulas.

Homework Statement



Projectile shot straight upwards, flight time = 4.70 sec
Second Launch at 45 degrees (horizontal range approx. 50-60 meters

A) Find Launch Velocity
B) Find Horizontal Range when shot at 45 degrees

Homework Equations



d = vit +1/2gt2

V = - 1/2gt ("made" this one myself from above formula, unsure if correct)

The Attempt at a Solution




Launch velocity

V = - 1/2gt
g = -9.8m/s
t = 4.7s

V = -[((1/2(-9.8))(4.7)]
V = -((-4.9)(4.7))
V = 23.0 m/sI have no idea how to calculate the horizontal range, I need a formula that incorperates the 45 degrees

Thanks in advance!

Homework Statement


Homework Equations


The Attempt at a Solution


You can work from first principles: Calculate the vertical and horizontal components of the launch speed - using sin45 and cos 45 factors.
The vertical component let's you calculate the flight time, the horizontal component with that time let's you calculate how far away it will land - the range.
Many Physics texts will have a section where a formula is derived, so you can simply substitute the 23 m/s to get an answer [assuming 23 m/s is correct - it certainly is a reasonable answer]
 
  • #3
PeterO said:
You can work from first principles: Calculate the vertical and horizontal components of the launch speed - using sin45 and cos 45 factors.
The vertical component let's you calculate the flight time, the horizontal component with that time let's you calculate how far away it will land - the range.

How would I do this? I am completely new to this and need a formula with a simple step-by-step guide on how to implement that formula to derive the answer.
 

FAQ: Projectiles: Launch speed and horizontal distance

1. How does launch speed affect the horizontal distance of a projectile?

The launch speed of a projectile directly affects its horizontal distance. The higher the launch speed, the farther the projectile will travel before hitting the ground. This is because the initial velocity of the projectile determines how fast it is moving horizontally, and therefore, how far it can travel in a given amount of time.

2. What is the ideal launch speed for maximum horizontal distance?

The ideal launch speed for maximum horizontal distance depends on the angle at which the projectile is launched. In general, a launch angle of around 45 degrees will result in the maximum horizontal distance. However, this may vary depending on air resistance and other factors.

3. How does air resistance affect the relationship between launch speed and horizontal distance?

Air resistance can significantly affect the relationship between launch speed and horizontal distance. As the speed of the projectile increases, so does the amount of air resistance it experiences. This can cause the projectile to slow down and not travel as far as it would without air resistance.

4. Are there any other factors that can influence the horizontal distance of a projectile besides launch speed?

Yes, there are other factors that can influence the horizontal distance of a projectile. These include the angle of launch, air resistance, the mass and shape of the projectile, and the gravitational force of the Earth. All of these factors must be taken into account when calculating the horizontal distance of a projectile.

5. How can we use the relationship between launch speed and horizontal distance to improve the accuracy of projectiles?

By understanding the relationship between launch speed and horizontal distance, we can make more accurate predictions about where a projectile will land. This can be especially useful in fields such as sports or military operations, where precise targeting is crucial. By adjusting the launch speed and angle, we can increase the chances of the projectile hitting its intended target with more accuracy.

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