You are standing on a bridge and drop a
rock into the water . With a
stopwatch you determine that it took
5.4 seconds to hit the water. The
acceleration due to gravity is

What is the height of the bridge? 466.56 ft
What is the velocity upon impact? [? ]
Give a decimal answer.

Ask by Garza Rojas. in the United States

Mar 17,2025

Question

You are standing on a bridge and drop a
rock into the water . With a
stopwatch you determine that it took
5.4 seconds to hit the water. The
acceleration due to gravity is

What is the height of the bridge? 466.56 ft
What is the velocity upon impact? [? ]
Give a decimal answer.

Ask by Garza Rojas. in the United States

Mar 17,2025

UpStudy AI · Accepted Answer

We are given:
- Initial velocity: $$ v(0)=0 $$
- Acceleration: $$ a(t) = -32\, \text{ft/sec}^2 $$
- Time to impact: $$ t = 5.4\, \text{sec} $$

The velocity as a function of time is found by integrating the acceleration:
$$
v(t) = v(0) + \int_0^t a(s)\, ds = 0 + \int_0^t (-32)\, ds = -32t
$$

Substitute $$ t = 5.4 $$ seconds:
$$
v(5.4) = -32 \times 5.4 = -172.8\, \text{ft/sec}
$$

Thus, the velocity upon impact is $$ -172.8\, \text{ft/sec} $$.
The velocity upon impact is $$ -172.8 \, \text{ft/sec} $$.