A wrench falls out of the gondola of a balloon
that is 830 m above the ocean.
Assuming negligible air resistance, what
was the wrench’s speed as it hit the water?
The acceleration of gravity is 9.8 m/s2 .
Answer in units of m/s
V = sqrt(2*g*H)
g = 9.8 m/s^2
H = 830 m
Use the above formula for the final velocity, V.
127.546
To determine the speed at which the wrench hit the water, we can use the principles of motion under gravity. Here's how you can calculate it:
1. Identify the relevant information:
- Initial vertical position (h) = 830 m
- Acceleration due to gravity (g) = 9.8 m/s^2 (downwards)
2. Calculate the time taken for the wrench to fall:
We can use the kinematic equation for vertical motion: h = (1/2)gt^2, where t is the time taken.
Rearranging the equation:
830 m = (1/2) * 9.8 m/s^2 * t^2
Solving for t:
t^2 = (830 m * 2) / 9.8 m/s^2
t^2 = 169.39 s^2
t ≈ √169.39
t ≈ 13.02 seconds
3. Calculate the final vertical velocity of the wrench:
Using the equation: v = gt, where v is the vertical velocity at time t.
v = 9.8 m/s^2 * 13.02 s
v ≈ 127.60 m/s (rounded to two decimal places)
Thus, the wrench's speed as it hits the water is approximately 127.60 m/s.