Calculating the Height of a Bridge
Billy-Joe stands on the Talahatchee Bridge
If Billy-Joe kicks a stone with a horizontal velocity of 3.5 m/s
If Billy-Joe kicks a stone with a horizontal velocity of 3.5 m/s and it lands in the water a horizontal distance of 5.4 m from where Billy-Joe is standing, we can calculate the height of the bridge.Calculation
To find the height of the bridge, first, we need to calculate the time of flight of the stone. This is done by analyzing the horizontal motion, which is a uniform motion with a constant velocity of 3.5 m/s. The time of flight is given by the equation:t = d / v
t = time of flight
d = horizontal distance covered by the stone (5.4 m)
v = horizontal velocity of the stone (3.5 m/s)
Substituting the values gives:t = 5.4 / 3.5 = 1.54 seconds
Now, we can analyze the vertical motion of the stone, which is a uniform accelerated motion with a constant acceleration of 9.8 m/s^2 downward. The height of the bridge can be calculated using the equation:h = ut + 1/2 * g * t^2
Where:h = height of the bridge (to be found)
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (9.8 m/s^2)
t = time of flight (1.54 seconds)
Substituting the values gives:h = 0 + 1/2 * 9.8 * (1.54)^2 = 11.6 meters
Question: What is the height of the Talahatchee Bridge if Billy-Joe kicks a stone with a horizontal velocity of 3.5 m/s and it lands 5.4 meters away from where he is standing? Answer: The height of the Talahatchee Bridge is 11.6 meters.