A rock thrown horizontally from the top of a radio tower lands 20.0 m from the base of the tower. If the speed at which the object was projected was 11.50 m/s, how high is the tower?
To find the height of the tower, we can use the kinematic equation for vertical motion. In this case, the rock is thrown horizontally, so there is no initial vertical velocity.
The equation we can use is:
y = (1/2)gt^2
Where:
y = vertical displacement (height of the tower)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken for the rock to fall to the ground
To find the time taken for the rock to fall, we can use the horizontal distance that the rock travels and the horizontal component of its velocity.
The time can be calculated using the equation:
t = distance / velocity
Given:
distance = 20.0 m
velocity = 11.50 m/s
Substituting these values, we can calculate the time taken:
t = 20.0 m / 11.50 m/s = 1.7391 s (rounded to four decimal places)
Now, we can substitute the calculated time (t) back into the equation for vertical displacement (y) to find the height of the tower:
y = (1/2) * 9.8 m/s^2 * (1.7391 s)^2
Calculating this, we get:
y ≈ 15.9604 m
Therefore, the height of the tower is approximately 15.9604 meters.
The leaning tower of Pisa is 55m high and 7m in diameter. The top of the tower
is displaced 4.5m from the vertical. Treat the tower as a uniform circular cylinder. (a)
What additional displacement measured from the top would bring the tower to the
verge of toppling? (b) What angle would the tower make with the vertical?