To solve this problem, we can use the equations of motion to calculate the time during which the stone is in motion, the distance from the tower base where the stone will drop to the ground, the velocity with which it will touch the ground, and the angle formed by the trajectory of the stone with the horizontal at the point where it reaches the ground.
First, let's find the time during which the stone is in motion. We can use the equation:
h = (1/2) * g * t^2
where h is the height of the tower, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. Rearranging the equation, we have:
t = sqrt((2 * h) / g)
Substituting the given values, we find:
t = sqrt((2 * 25) / 9.8) ≈ 2.26 s
Next, let's calculate the distance from the tower base where the stone will drop to the ground. We know that the horizontal velocity of the stone remains constant throughout its motion. The distance traveled horizontally is given by:
d = v * t
where d is the distance, v is the horizontal velocity, and t is the time. Substituting the given values, we have:
d = 15 * 2.26 ≈ 33.9 m
Now, let's calculate the velocity with which the stone will touch the ground. The vertical component of the velocity can be found using the equation:
v = g * t
where v is the vertical velocity, g is the acceleration due to gravity, and t is the time. Substituting the given values, we have:
v = 9.8 * 2.26 ≈ 22.1 m/s
The total velocity with which the stone will touch the ground can be found using the Pythagorean theorem:
V = sqrt(v_horizontal^2 + v_vertical^2)
where V is the total velocity, v_horizontal is the horizontal velocity, and v_vertical is the vertical velocity. Substituting the given values, we have:
V = sqrt(15^2 + 22.1^2) ≈ 26.75 m/s
Finally, let's calculate the angle formed by the trajectory of the stone with the horizontal at the point where it reaches the ground. We can use the equation:
tan(theta) = v_vertical / v_horizontal
where theta is the angle. Substituting the given values, we have:
tan(theta) = 22.1 / 15
Taking the inverse tangent of both sides, we find:
theta ≈ 55°
Comparing our calculations with the answer choices, we find that the correct option is a) 2.26 s, 33.9 m, 26.75 m/s, 55°.