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 9.9 m/s. If he is 35 m above the catapult, what is the initial velocity of the boulders? Theacceleration of gravity is 9.8 m/s
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Use
v1^2-v0^2 = 2aS
v1=final velocity
v0=initial velocity
a=acceleration
S=distance
Use an appropriate frame of reference such as positive = upwards.
To solve this problem, we can use the kinematic equation for vertical motion:
v^2 = u^2 + 2as
Where:
v = final velocity (in this case, the vertical velocity of the boulder when it lands on the wall)
u = initial velocity (what we want to find)
a = acceleration (in this case, the acceleration due to gravity, which is -9.8 m/s^2)
s = vertical displacement (the height from the catapult to the wall, which is 35 m)
We can rearrange the equation to solve for the initial velocity (u):
u^2 = v^2 - 2as
Plugging in the given values:
u^2 = (9.9 m/s)^2 - 2(-9.8 m/s^2)(35 m)
Calculating:
u^2 = 97.01 m^2/s^2 + 686 m^2/s^2
u^2 = 783.01 m^2/s^2
Taking the square root of both sides:
u = √783.01 m/s
Therefore, the initial velocity of the boulders is approximately 28 m/s.
To find the initial velocity of the boulders, we can use the kinematic equation for vertical motion:
v^2 = u^2 + 2as
where:
v = final velocity (which is 9.9 m/s, as given)
u = initial velocity (what we need to find)
a = acceleration due to gravity (which is -9.8 m/s^2)
s = vertical displacement (which is the height of the castle wall, 35 m)
Plugging in the values into the equation, we have:
9.9^2 = u^2 + 2(-9.8)(35)
Simplifying, we get:
98.01 = u^2 - 686
Rearranging the equation to solve for u^2, we have:
u^2 = 98.01 + 686
u^2 = 784.01
Taking the square root of both sides, we find:
u ≈ 28 m/s
Therefore, the initial velocity of the boulders is approximately 28 m/s.