Can someone please tell me the right answer to this problem.
A troll on a 75m tall cliff throws a 35 m/s boulder at 35 degrees above the horizontal at a herd of sheep. What is the time of flight, the range and the maximum height for the boulder?
I got the range as 58.77. and the max. height to be 20.58. if i did it wrong can someone PLEASEEEEEEEEEE help me! thanks so much:)
The range is 58.77. and the max is also 20.58. You did it right. Because I even wrote it down and I used my calculator. So, yes you did it correctly.
Rachael can you please show me your work?
To find the time of flight, range, and maximum height of the boulder, we can use the equations of projectile motion. Let's go through each calculation step by step.
1. Time of Flight:
The time of flight is the total duration the boulder is in the air. We can calculate it using the vertical component of the initial velocity and the acceleration due to gravity. The formula to find the time of flight is:
time = (2 * initial vertical velocity) / acceleration due to gravity
In this case, the vertical component of the initial velocity is given by:
initial vertical velocity = initial velocity * sin(angle)
Using given values, we have:
initial velocity = 35 m/s
angle = 35 degrees
Calculating the initial vertical velocity:
initial vertical velocity = 35 m/s * sin(35 degrees)
≈ 20.066 m/s
Now, we can calculate the time of flight:
time = (2 * 20.066 m/s) / 9.8 m/s^2
≈ 4.09 seconds
Therefore, the time of flight is approximately 4.09 seconds.
2. Range:
The range is the horizontal distance covered by the boulder. We can calculate it using the horizontal component of the initial velocity and the time of flight. The formula to find the range is:
range = initial horizontal velocity * time
The horizontal component of the initial velocity is given by:
initial horizontal velocity = initial velocity * cos(angle)
Calculating the initial horizontal velocity:
initial horizontal velocity = 35 m/s * cos(35 degrees)
≈ 28.735 m/s
Now, we can calculate the range:
range = 28.735 m/s * 4.09 s
≈ 117.63 meters
Therefore, the range is approximately 117.63 meters.
3. Maximum Height:
The maximum height represents the highest point reached by the boulder during its flight. We can calculate it using the vertical component of the initial velocity and the time of flight. The formula to find the maximum height is:
maximum height = (initial vertical velocity^2) / (2 * acceleration due to gravity)
Using the initial vertical velocity calculated earlier (20.066 m/s), we can calculate the maximum height as follows:
maximum height = (20.066 m/s)^2 / (2 * 9.8 m/s^2)
≈ 20.52 meters
Therefore, the maximum height is approximately 20.52 meters.
To summarize:
- The time of flight is approximately 4.09 seconds.
- The range is approximately 117.63 meters.
- The maximum height is approximately 20.52 meters.
Please note that these calculations assume a flat surface and negligible air resistance.