A tennis ball thrown horizontally from the top of a water tower lands 20.0m from the base of the tower. The tennis ball is initially thrown at a velocity of 10.0m/s.
a) How high is the water tower?
b) How long does it take for the ball to hit the ground?
To solve this problem, we can use the kinematic equations of motion. Let's denote the height of the water tower as h.
a) To find the height of the water tower, we need to determine the time it takes for the ball to hit the ground. Since the ball is thrown horizontally, there is no vertical acceleration acting on it. Therefore, the initial vertical velocity is zero (v0y = 0).
The equation we can use to determine the time is:
h = v0y * t + (1/2) * g * t^2
Since v0y = 0, the equation simplifies to:
h = (1/2) * g * t^2
We also know that the horizontal distance travelled is 20.0 m, which can be expressed as:
d = v0x * t
where v0x is the horizontal velocity (10.0 m/s) and t is the time taken to hit the ground.
Substituting v0x into the equation, we have:
d = 10.0 * t
t = d / 10.0
t = 20.0 / 10.0
t = 2.0 s
Now that we know the time taken to hit the ground, we can substitute it back into the equation for height:
h = (1/2) * g * t^2
h = (1/2) * 9.8 * (2.0)^2
h = 19.6 m
The water tower is 19.6 m high.
b) To find the time it takes for the ball to hit the ground, we can use the horizontal distance travelled and the horizontal velocity:
d = v0 * t
Solving for t:
t = d / v0
t = 20.0 / 10.0
t = 2.0 s
It takes 2.0 seconds for the ball to hit the ground.