Projectile Motion without Initial Velocity

In summary, the problem involves a projectile launched at an angle of 50° above the horizontal, hitting the ground in 12 seconds. The goal is to find the maximum height and range of the projectile, but these calculations require the initial velocity, which is not provided. The solution involves using the given formula for maximum height and solving for initial velocity using the formula for vertical velocity. Once the vertical velocity is known, the initial velocity can be found using trigonometry.
  • #1
PerryKid
12
0
Projectile Motion without Initial Velocity (Only time and angle given)

Homework Statement



A projectile is launched at an angle of 50° above the horizontal and it hits the ground in 12 seconds.

a. Calculate the maximum height of the projectile.
b. Find the range of the projectile.

Homework Equations



[itex]H_{max}=\frac{V_{o}^{2}+sin^{2}\theta}{g}[/itex]

[itex]R=V_{o}\sqrt{\frac{2H}{g}}[/itex]

The Attempt at a Solution



I don't know where to start. I can't solve without Vo and I am missing Vo.
 
Last edited:
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  • #2
Can you not use a standard kinematic equation to get vy0?
 
  • #3
I need [STRIKE]Vo to find height and range, not Vyo[/STRIKE]

EDIT: I found a formula to help me solve it all! :approve:

[itex]V_{y}=V_{o}Sin(\theta)-gt[/itex]

[itex]V_{y}=0[/itex]
 
  • #4
But if you can find vy0, then you can find v0 with some simple trig.
 
  • #5
PerryKid said:
EDIT: I found a formula to help me solve it all! :approve:

[itex]V_{y}=V_{o}Sin(\theta)-gt[/itex]

[itex]V_{y}=0[/itex]

That will work. At what t will vy = 0?
 

Related to Projectile Motion without Initial Velocity

1. What is projectile motion without initial velocity?

Projectile motion without initial velocity is a type of motion in which an object is launched or thrown without any initial velocity or force acting on it. This means that the object starts at rest and its motion is solely influenced by the force of gravity.

2. How is the trajectory of an object affected in projectile motion without initial velocity?

In this type of motion, the trajectory of the object will be a parabola, as the force of gravity will act on it equally in both the vertical and horizontal directions. The object will follow a curved path and eventually fall back to the ground due to the acceleration of gravity.

3. Can an object reach its maximum height in projectile motion without initial velocity?

Yes, an object can reach its maximum height in this type of motion. However, the maximum height will be lower than in cases where the object has an initial velocity. This is because the initial velocity also contributes to the height the object can reach.

4. How does air resistance affect projectile motion without initial velocity?

In ideal conditions, without any air resistance, the object will follow a perfect parabolic path. However, in reality, air resistance will affect the object's motion and cause it to deviate from the ideal parabolic path. This can also result in a decrease in the object's maximum height and range.

5. Can you calculate the speed of an object in projectile motion without initial velocity?

Yes, it is possible to calculate the speed of an object in this type of motion. The speed can be determined by using the equation v = gt, where v is the final velocity, g is the acceleration of gravity (9.8 m/s^2), and t is the time the object has been in motion. However, without knowing the initial velocity, the final velocity will be solely dependent on the time the object has been in motion.

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