Projectile motion- height of building

[Maiia]

Homework Statement

Take up as positive. A rock is projected from the edge of the top of a building with an initial velocity of 16.5 m/s at an angle of 40 degrees above the horizontal. The rock strikes the ground a horizontal distance of 82m from the base of the building. The acceleration of gravity is 9.8m/s2. Assume the ground is level and that the side of the building is vertical. Neglect air friction.

How tall is the building? Answer in units of m.

Homework Equations

delta X= Vxt
Vy= V0y + ayt
Yf-yi= V0yt + 1/d ayt2

The Attempt at a Solution

For this problem, I already found the horizontal component of the rock's velocity when it strikes the ground and the time the rock stays airborne. However, I'm not quite sure how to find the height of the building. I tried doing it this way: Use equation 3, substituting 0 for yi (ground level) and the ycomponent of velocity, and the acceleration as -9.8 to solve for Yf. Is my process right? Because when I solve for Yf, I get 275.0343353, which according to quest, is wrong.

 

[buffordboy23]

The rock will follow a parabolic trajectory. The y-component of the velocity will equal zero for a brief moment at the highest point of the parabola. Does this help?

 

[Maiia]

So are you suggesting that I set Vyf= 0 and Vyi= V0sinθ? But if I do that, won't that give me the delta y of the entire distance from the peak of the parabola to the ground when I only need to find the height of the building?

 

[buffordboy23]

You know the total time that the rock is in the air. Performing my suggestion should give you the time for the rock to reach its apex, and also the time for it to fall from the apex to the ground.

 

[Maiia]

oh so you double that time then subtract from t total then plug that into the equation.

 

[Maiia]

if you wanted to find the vertical component of the rock's velocity when it hits the ground, you would use that delta y, right?

 

[buffordboy23]

if you wanted to find the vertical component of the rock's velocity when it hits the ground, you would use that delta y, right?

You could, if you knew values of all of the appropriate variables. You could also use the second equation that you wrote, since we know all the variables except Vy.