An object fired horizontally with a velocity of 30m/s from a top of a taal tower 250m high.The object lands on top of a building which is 174m away from the tower.How high is the building.(g=10m/s^2)
654m/s
81.8
To find the height of the building, we can use the equations of motion for a horizontally launched projectile.
First, let's identify the given values:
Initial velocity (u) = 30 m/s (horizontal)
Height of the tower (h) = 250 m
Distance from the tower to the building (d) = 174 m
Acceleration due to gravity (g) = 10 m/s^2
Step 1: Find the time of flight (t) of the projectile.
We can use the equation: h = ut + (1/2)gt^2
Substituting the given values:
250 = 0*t + (1/2)(10)(t^2)
Simplifying the equation:
5t^2 = 250
Dividing by 5:
t^2 = 50
Taking the square root of both sides:
t ≈ 7.07 seconds
Step 2: Find the horizontal distance traveled (x) by the projectile.
We can use the equation: x = u*t
Substituting the given values:
x = (30 m/s)*(7.07 s)
x ≈ 212.10 meters
Step 3: Calculate the height of the building.
The horizontal distance traveled by the projectile is equal to the distance from the tower to the building.
Therefore, the height of the building is the height of the tower minus the height covered by the projectile in the horizontal distance.
Height of the Building (H) = Height of the tower (h) - Horizontal distance traveled (x)
H = 250 - 212.10
H ≈ 37.90 meters
So, the height of the building is approximately 37.90 meters.
To find the height of the building, we can first determine the time it takes for the object to reach the building. We can then use this time to calculate the vertical distance the object falls during this time.
1. Calculate the time of flight:
Since the object is fired horizontally, there is no initial vertical velocity. Therefore, the time taken to reach the building can be found using the horizontal distance and horizontal velocity.
Time = Distance / Velocity
Time = 174 m / 30 m/s = 5.8 seconds
2. Calculate the vertical distance fallen:
The object falls vertically under the influence of gravity during the time of flight. We can calculate the vertical distance using the equation of motion:
h = (1/2) * g * t^2
where h is the initial height, g is the acceleration due to gravity, and t is the time of flight.
h = (1/2) * 10 m/s^2 * (5.8 s)^2
h = 10 * 16.84
h ≈ 168.4 m
Therefore, the height of the building is approximately 168.4 meters.