Joe stands on a bridge kicking stones into the water below. If he kicks a stone with a horizontal velocity of 3.10 m/s, and it lands in the water a horizontal distance of 6.60 m from where Joe is standing, what is the height of the bridge? Enter m as unit. Draw the problem.
To solve this problem, we can use the following steps:
Step 1: Draw a diagram illustrating the information given in the question.
Consider a bridge with Joe standing on it. Let's mark Joe's position as Point A. Joe kicks a stone that lands in the water, which we can indicate as Point B. The horizontal distance between A and B is given as 6.60 m.
```
A ***********
|______| 6.60 m
B
```
Step 2: Identify the known variables in the problem:
- Horizontal velocity (Vx) = 3.10 m/s
- Horizontal distance (Δx) = 6.60 m
Step 3: Determine the time it takes for the stone to travel from Joe's position to the water.
We know that the horizontal distance (Δx) is related to the horizontal velocity (Vx) and the time (t) as follows:
Δx = Vx * t
Applying this equation, we can solve for time:
t = Δx / Vx
Plugging in the values:
t = 6.60 m / 3.10 m/s
Step 4: Calculate the time (t).
t = 2.13 s (rounded to two decimal places)
Step 5: Find the height of the bridge.
To find the height of the bridge, we need to determine the vertical component of the stone's velocity when it hits the water.
Since we have the time and the horizontal velocity, we can use the formula:
Vy = g * t
Where:
- Vy: Vertical velocity
- g: Acceleration due to gravity (approximately 9.8 m/s^2)
- t: Time
Plugging in the values:
Vy = 9.8 m/s^2 * 2.13 s
Step 6: Calculate the vertical velocity (Vy).
Vy = 20.86 m/s (rounded to two decimal places)
Step 7: Determine the height of the bridge.
The height of the bridge can be calculated using the formula:
Height = 0.5 * g * t^2
Plugging in the values:
Height = 0.5 * 9.8 m/s^2 * (2.13 s)^2
Step 8: Calculate the height of the bridge.
Height = 21.10 m (rounded to two decimal places)
Therefore, the height of the bridge is approximately 21.10 m.
Dx = Xo*t = 6.6 m.
3.1t = 6.6,
t = Tf = 2.13 s. = Fall time = Time in flight.
h = Vo*t + 0.5g*t^2,
h = 0 + 4.9(2.13)^2 = 22.2 m.