Answer:
40.1 m
Explanation:
Objects in free fall, or projectiles, undergo constant acceleration. Using kinematics, we can write equations that relate the displacement, velocity, acceleration, and time. One kinematic equation is:
s = ut + ½ at²
where s is displacement, u is initial velocity, a is acceleration, and t is time. Since the initial velocity is zero, this simplifies to:
s = ½ at²
If h is the height of the tower, and t is the total time it takes to fall, and the acceleration is a = 10 m/s², then:
h = 5t²
Similarly, the body falls a distance of h − 40 meters in the first t − 2.71 seconds, so we can write a second equation:
h − 40 = 5 (t − 2.71)²
Substituting and solving for time:
5t² − 40 = 5 (t − 2.71)²
t² − 8 = (t − 2.71)²
t² − 8 = t² − 5.42 t + 7.34
0 = -5.42 t + 15.34
t = 2.83
Therefore, the height of the tower is:
h = 5t²
h = 5 (2.83)²
h = 40.1
