A water balloon is dropped from the top of a 65.0m tall building.
What is its final velocity just before it hits the ground?
How long does it take to hit the ground?
a. V^2 = Vo^2 + 2g*h = 0 + 19.6*65 =
V = ?
b. h = 0.5g*t^2 = 65.
4.9*t^2 = 65.
To solve for the final velocity and the time it takes to hit the ground, we can use the equations of motion.
Step 1: Calculate the acceleration due to gravity.
The acceleration due to gravity is a constant value of approximately 9.8 m/s².
Step 2: Solve for the final velocity.
Using the equation of motion: v² = u² + 2as,
where v is the final velocity, u is the initial velocity (0 m/s as it was dropped), a is the acceleration due to gravity, and s is the displacement (65.0m).
v² = 0² + 2(9.8)(65.0)
v² = 0 + 1274
v ≈ √1274
v ≈ 35.7 m/s
Step 3: Solve for the time taken to hit the ground.
Using the equation of motion: s = ut + 0.5at²,
where s is the displacement (65.0m), u is the initial velocity (0 m/s), a is the acceleration due to gravity, and t is the time taken.
65.0 = 0( t) + 0.5(9.8)(t²)
65.0 = 4.9t²
t² = 65.0/ 4.9
t² ≈ 13.3
t ≈ √13.3
t ≈ 3.65 s
Therefore, the final velocity just before the water balloon hits the ground is approximately 35.7 m/s, and it takes approximately 3.65 seconds to hit the ground.
To find the final velocity of the water balloon just before it hits the ground, we can use the equation for free fall:
v = √(2gh)
Where:
v = final velocity
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height from which the object is dropped
Now, let's calculate the final velocity of the water balloon:
v = √(2 × 9.8 m/s² × 65.0 m)
v ≈ √(1274 m²/s²)
v ≈ 35.7 m/s
Therefore, the final velocity of the water balloon just before hitting the ground is approximately 35.7 m/s.
To find the time it takes for the water balloon to hit the ground, we can use the equation:
h = (1/2)gt²
Where:
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height from which the object is dropped
t = time taken to hit the ground
Rearranging the equation, we get:
t = √(2h/g)
Now, let's calculate the time it takes for the water balloon to hit the ground:
t = √(2 × 65.0 m / 9.8 m/s²)
t ≈ √(13.3 s²)
t ≈ 3.65 s
Therefore, it takes approximately 3.65 seconds for the water balloon to hit the ground.