A knight sits on a castle wall during a siege.To while away the time, he notes that boulders catapulted from below land on the top of his wall with a vertical velocity of 5.7 m/s. If he is 45 m above the catapult, what is the initial velocity of the boulders? The acceleration of gravity is 9.8 m/s 2.
How do I find the answer if all I have is final velocity and accleration?
To find the initial velocity of the boulders, we can use the kinematic equation that relates displacement, initial velocity, final velocity, acceleration, and time:
Final velocity (vf) = initial velocity (vi) + acceleration (a) * time (t)
In this scenario, the final velocity is the vertical velocity of the boulders, which is 5.7 m/s, the acceleration is the acceleration due to gravity (9.8 m/s²), and the time is unknown.
Since the boulders are launched from the catapult at ground level and reach a height of 45 m on the castle wall, this can be considered a projectile motion. We can use the kinematic equation for vertical displacement to find the time it takes for the boulders to reach the top of the wall:
Vertical displacement (Δy) = initial vertical velocity (viy) * time (t) + (1/2) * acceleration (a) * time² (t²)
In this case, the vertical displacement is 45 m, the initial vertical velocity is unknown, the acceleration is the acceleration due to gravity (-9.8 m/s² since it acts in the opposite direction of the boulders' motion), and we are solving for the time.
We can rearrange the equation for vertical displacement to solve for time:
45 m = (viy) * t - (1/2) * (9.8 m/s²) * t²
To solve this quadratic equation, we can either factor it or use the quadratic formula. Once we find the time, we can substitute it back into the first equation to calculate the initial velocity of the boulders.
Please note that if any other information is available, such as the horizontal distance traveled by the boulders, it can be used to calculate the initial velocity as well.