(a) Well, let's see. The stone was thrown horizontally from the top of an 18-meter tower, and it hits the ground at a point 18 meters from the base of the tower. Now, if we ignore any effects due to air resistance, we can assume that the stone will travel in a straight line horizontally until it hits the ground. So, the time it takes for the stone to hit the ground is the same as the time it takes for the stone to travel horizontally 18 meters.
We can use the equation d = vt, where d is the distance, v is the velocity, and t is the time. In this case, d is 18 meters and v is what we are trying to find. We can assume that the time taken is the same, so we have:
18 = v * t
Since the stone was thrown horizontally, there is no vertical acceleration, and the only horizontal force is gravity. So, the time taken for the stone to hit the ground is the same as the time it would take for an object to fall 18 meters vertically.
Using the formula h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity, and t is the time, we can solve for time. Plugging in the values, we have:
18 = (1/2)(9.8)t^2
Multiplying both sides by 2 and dividing by 9.8, we get:
36/9.8 = t^2
t^2 = 36/9.8
Taking the square root of both sides, we have:
t = √(36/9.8)
Plugging this value of t back into the first equation, we get:
18 = v * √(36/9.8)
Now, solving for v:
v = 18 / √(36/9.8)
Calculating this, we find:
v ≈ 12.26 m/s
So, the speed at which the stone was thrown is approximately 12.26 m/s.
(b) Now, to find the speed of the stone just before it hits the ground, we can use the same equation, d = vt, but this time the distance is 18 meters (the distance from the base of the tower to the point where the stone hits the ground) and the time is the same as before. Plugging in these values, we have:
18 = v * √(36/9.8)
Now solving for v:
v = 18 / √(36/9.8)
Calculating this, we find:
v ≈ 12.26 m/s
So, the speed of the stone just before it hits the ground is also approximately 12.26 m/s.
Looks like the stone maintained its speed all the way down! Talk about consistency!