From your vantage point on the roof of your 6.5 m tall apartment building you are launching water balloons over the 3.5 m wall at the back of your complex. The large singlshot is launching the balloons horizontally such that they just barely clear the wall 12m away. (a) How long does it take the balloon to reach the top of the wall? (b) What is the initial speed of the balloon? (c) What is the speed of the balloon as it clears the wall?
To find the answers to these questions, we need to analyze the motion of the water balloon and apply the equations of motion.
(a) To calculate the time it takes for the balloon to reach the top of the wall, we can use the equation for vertical motion:
h = ut + (1/2)gt²
Where:
h = height (6.5 m in this case)
u = initial vertical velocity (0 m/s, since the balloon is launched horizontally)
g = acceleration due to gravity (-9.8 m/s²)
t = time
Since the balloon is launched horizontally, it does not have an initial vertical velocity. Therefore, the equation simplifies to:
h = (1/2)gt²
Plugging in the values, we get:
6.5 = (1/2)(-9.8)t²
Rearranging the equation, we have:
3.25 = -4.9t²
Now, we can solve for time (t):
t² = 3.25 / -4.9
t = √(-0.663)
Since square root of a negative number is not physically meaningful, it means that the water balloon does not reach the top of the wall.
(b) To find the initial speed of the water balloon, we can use the horizontal distance it travels (12 m) and the time it takes to reach that distance.
d = ut
12 = u * (t_total)
We can rearrange this equation to solve for the initial speed (u):
u = d / t
u = 12 m / t
Since we have already determined that the balloon does not reach the top of the wall and also cleared the wall, we don't have a specific value for the total time (t_total). Therefore, we cannot calculate the exact initial speed (u).
(c) As the balloon clears the wall, its horizontal velocity remains constant. So, the speed of the balloon as it clears the wall is equal to its horizontal speed.
In this case, we do not have any information about the balloon's horizontal velocity or time taken to travel 12 m. Hence, we cannot determine the exact speed of the balloon as it clears the wall.