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 7.5 m/s. If he is 34 m above the catapult, what is the initial velocity of the boulders? The acceleration of gravity is 9.8 m/s^2.Answer in units of m/s. Shouldnt the answer be 24.7?
To find the initial velocity of the boulders, we can use the kinematic equation:
v_f^2 = v_i^2 + 2aΔy
Where:
- v_f is the final velocity (which is 7.5 m/s, since the boulders have a vertical velocity of 7.5 m/s)
- v_i is the initial velocity (what we are trying to find)
- a is the acceleration due to gravity (-9.8 m/s^2, negative because it acts downwards)
- Δy is the displacement in the vertical direction (34 m, since the knight is 34 m above the catapult)
Substituting the given values into the equation, we have:
(7.5 m/s)^2 = v_i^2 + 2 * (-9.8 m/s^2) * 34 m
Simplifying the equation, we get:
56.25 m^2/s^2 = v_i^2 - 660.8 m^2/s^2
Rearranging the equation to solve for v_i^2, we have:
v_i^2 = 56.25 m^2/s^2 + 660.8 m^2/s^2
v_i^2 = 717.05 m^2/s^2
Taking the square root of both sides to solve for v_i, we get:
v_i = √(717.05 m^2/s^2)
v_i ≈ 26.78 m/s
Therefore, the initial velocity of the boulders is approximately 26.78 m/s. So, the answer is not 24.7 m/s, but rather around 26.78 m/s.