Projectile motion- height of building

In summary, the problem involves a rock being projected from the top of a building with a known initial velocity and angle, and striking the ground a known distance away. To find the height of the building, one can use the equation for vertical displacement and set the final velocity to zero, or use the total time the rock is in the air to find the time it takes to reach its apex and fall back down. The vertical component of the rock's velocity can then be found using the second equation.
  • #1
Maiia
79
0

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.
 
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  • #2
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?
 
  • #3
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?
 
  • #4
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.
 
  • #5
oh so you double that time then subtract from t total then plug that into the equation.
 
  • #6
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?
 
  • #7
Maiia said:
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.
 

1. What is projectile motion?

Projectile motion is a type of motion in which an object is thrown or launched into the air and moves in a curved path due to the influence of gravity.

2. How is the height of a building calculated using projectile motion?

The height of a building can be calculated using projectile motion by measuring the distance traveled by the object, the angle at which it was launched, and the acceleration due to gravity. Using these values, we can use the equation h = (v^2(sin^2(θ)))/(2g) to calculate the height of the building, where h is the height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

3. How accurate is projectile motion in determining the height of a building?

Projectile motion is a reliable method for calculating the height of a building, as long as the initial velocity and launch angle are measured accurately. However, factors such as air resistance and wind can affect the accuracy of the calculation.

4. Can projectile motion be used to calculate the height of any building?

Projectile motion can be used to calculate the height of any building as long as the necessary variables are known and measured accurately. However, it may not be the most practical method for very tall buildings or buildings with irregular shapes.

5. What other factors can affect the height calculation of a building using projectile motion?

In addition to air resistance and wind, other factors that can affect the height calculation of a building using projectile motion include the precision of the measurements, the launch surface, and the shape and size of the object being launched.

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