Maximum height of a projectile thrown from a rooftop

In summary, the man throws a rock from a building of height 14.6m with a velocity of 30.8m/s at an angle of 33.2∘ above the horizontal. Using velocity and position equations and basic trigonometry, the maximum height above the roof reached by the rock is 29.1m. However, the maximum height above the ground is actually 14.5m, as the rock was thrown from the top of the building.
  • #1
s.dyseman
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Homework Statement



A man stands on the roof of a building of height 14.6m and throws a rock with a velocity of magnitude 30.8m/s at an angle of 33.2∘ above the horizontal. You can ignore air resistance.

Calculate the maximum height above the roof reached by the rock.

Homework Equations



Velocity and position equations

Basic trigonometry

The Attempt at a Solution



Initially, I solved for the y-component of the velocity vector given: V=30.8*Sin(33.2)=16.86m/s

Then, I solved for the amount of time it would take for the rock to reach maximum height, where the velocity of the y-component vector is equal to 0: Vy=Voy+g*t=16.86-9.8t=1.72s

I plug this time into the position equation of Y=Yo+Voy*t+g*t^2=14.6+16.86(1.72)-4.9(1.72)^2=29.1m

So, the maximum height should be equal to 29.1m. Not sure why this is incorrect... Perhaps I calculated the vector incorrectly?
 
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  • #2
Calculate the maximum height above the roof reached by the rock.
You calculated the maximum height above the ground (and I can confirm this value).
 
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  • #3
Ah, so I just needed to subtract the height of the roof... Simple detail I missed... Thank you!
 

FAQ: Maximum height of a projectile thrown from a rooftop

What is the maximum height that a projectile can reach when thrown from a rooftop?

The maximum height of a projectile thrown from a rooftop is determined by the initial velocity, launch angle, and gravitational force acting on the object. It can be calculated using the formula: h = (v2sin2θ)/2g, where h is the maximum height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s2).

Does the mass of the projectile affect its maximum height?

Yes, the mass of the projectile does affect its maximum height. However, it is not a significant factor if the mass is small compared to the air resistance and gravitational force acting on the object.

What is the ideal launch angle to achieve the maximum height for a projectile thrown from a rooftop?

The ideal launch angle to achieve the maximum height for a projectile depends on the initial velocity and the gravitational force acting on the object. It can be calculated using the formula: θ = sin-1(√(2h/g)), where θ is the ideal launch angle, h is the maximum height, and g is the acceleration due to gravity.

Can air resistance affect the maximum height of a projectile thrown from a rooftop?

Yes, air resistance can affect the maximum height of a projectile thrown from a rooftop. The higher the air resistance, the lower the maximum height of the object will be. However, for most situations, the effect of air resistance is negligible and can be ignored.

How does the maximum height of a projectile thrown from a rooftop change with different initial velocities?

The maximum height of a projectile thrown from a rooftop increases with higher initial velocities. This is because a higher initial velocity means the object has more energy to overcome the gravitational force and reach a greater height. However, the change in maximum height is not directly proportional to the change in initial velocity, as other factors such as air resistance and launch angle also play a role.

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