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?
HOW DO I DO THIS??
You know the initial vertical velocity (35sin35).
Vf at top max height is zero. Use
vf=vivertical-gt to to find the time to the top, then use
h=ho+vivert*t-1/2 g t^2 to find the max height.
For time of flight, hf=0
0=ho+vivert*t-gt solve for t
now, having the time of flight, the horizontal distance will be
distance=vihoriz*t
is the correct answer for max height 20.58, and the correct answer for the range 58.77?
To find the time of flight, range, and maximum height of the boulder, we can use the equations of projectile motion. Here's how to calculate each value:
1. Time of Flight:
The time of flight is the total time it takes for the boulder to travel from the troll to the ground. We can use the equation:
time = (2 * initial vertical velocity) / (acceleration due to gravity)
First, let's find the initial vertical velocity of the boulder. We know that the boulder is thrown at 35 degrees above the horizontal at a speed of 35 m/s. We can calculate the initial vertical velocity using trigonometry:
initial vertical velocity = initial speed * sin(angle)
So, initial vertical velocity = 35 m/s * sin(35 degrees).
Next, we can substitute the value of acceleration due to gravity, which is approximately 9.8 m/s^2, into the time equation:
time = (2 * initial vertical velocity) / (acceleration due to gravity).
2. Range:
The range is the horizontal distance the boulder travels before hitting the ground. We can use the equation:
range = horizontal velocity * time of flight
To find the horizontal velocity, we can use trigonometry again:
horizontal velocity = initial speed * cos(angle)
So, horizontal velocity = 35 m/s * cos(35 degrees).
Now, we can substitute the values and calculate the range using the equation:
range = horizontal velocity * time of flight.
3. Maximum Height:
The maximum height is the highest point the boulder reaches during its trajectory. We can use the equation:
maximum height = (initial vertical velocity^2) / (2 * acceleration due to gravity)
Substitute the values and calculate the maximum height using the equation above.
By following these steps and performing the calculations, you can find the time of flight, range, and maximum height of the boulder.