Maximum height of a projectile

In summary, to calculate the maximum height above sea level of a projectile, you can use the equation sy=uyt-1/2gt² and substitute in the values for initial velocity, angle, and time of flight. To determine the time at which the projectile reaches its maximum height, you can use the equation H=(u^2 sin^2 A)/g and note that the vertical velocity is zero at this point.
  • #1
Bugsy23
25
0
I need to calculate the maximum height above sea level of a projectile. I already have the values for the initial velocity, the angle and the time of flight, and I have the following equation to calculate the y-component of the displacement from the launch point:
sy=uyt-1/2gt²
But how do I know at what time the projectile has reached its maximum height and begins accelerating downwards?
 
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  • #2
Bugsy23 said:
I need to calculate the maximum height above sea level of a projectile. I already have the values for the initial velocity, the angle and the time of flight, and I have the following equation to calculate the y-component of the displacement from the launch point:
sy=uyt-1/2gt²
But how do I know at what time the projectile has reached its maximum height and begins accelerating downwards?

Do you know any equations that relate initial velocity, acceleration, time and final velocity?
 
  • #3
Note the vertical velocity is zero at the maximum height...
 
  • #4
calculated it... H=(u^2 sin2A)/g
 
  • #5
Sakriya said:
calculated it... H=(u^2 sin2A)/g

Assuming you meant [itex] sin^2 A [/itex] and not sin(2A) it's correct, except
for a factor (1/2) that you're missing.
 

What is the definition of maximum height of a projectile?

The maximum height of a projectile is the highest vertical distance reached by the object during its flight before falling back to the ground.

What factors affect the maximum height of a projectile?

The maximum height of a projectile is affected by the initial velocity, angle of launch, and the force of gravity acting on the object.

How can the maximum height of a projectile be calculated?

The maximum height of a projectile can be calculated using the equation: h = (v2 sin2 θ) / (2g), where h is the maximum height, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

Can the maximum height of a projectile be greater than the initial height?

Yes, the maximum height of a projectile can be greater than the initial height if the angle of launch is greater than 45 degrees. This is because the vertical component of the initial velocity is greater than the horizontal component, allowing the object to reach a higher height.

How does air resistance affect the maximum height of a projectile?

Air resistance can decrease the maximum height of a projectile, as it acts to slow down the object's vertical motion. This is more significant for projectiles with larger surface areas, such as a feather, compared to smaller and more aerodynamic objects, such as a bullet.

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