In many locations, old abandoned stone quarries have become filled with water once excavating has been completed. While standing on a quarry wall, a boy tosses a piece of granite into the water below. If he throws the rock horizontally with a velocity of 3.0 m/s and it strikes the water 4.5 m from the base of the wall, how high above the water is the wall?
Alright I think figured out that time = 1.5s
because D = VT
4.5m = 3.0 m/s * T
but where do I go from here?
Dh = Vt,
T = Dh/V = 4.5/3 = 1.5s. = Time in flight = Fall time.
h = Vo*t + 0.5g*t^2,
h = 0 + 4.9(1.5)^2 = 11.03m.
To calculate the height of the wall above the water, you need to determine the time it takes for the rock to hit the water. Once you have the time, you can use the equations of motion to find the height of the wall.
Given that the horizontal velocity of the rock is 3.0 m/s and it lands 4.5 m from the base of the wall, you have already correctly determined that the time is 1.5 s using the equation:
Distance (D) = Velocity (V) × Time (T)
Now, to find the height of the wall above the water, you can use the equation of motion for vertical displacement:
Vertical Displacement (S) = Initial Vertical Velocity (U) × Time (T) + 0.5 × Acceleration (A) × Time^2
Since the rock is thrown horizontally, the initial vertical velocity (U) is 0 m/s. The acceleration due to gravity (A) is approximately 9.8 m/s^2 (assuming no air resistance).
Therefore, the equation becomes:
Vertical Displacement (S) = 0.5 × 9.8 m/s^2 × (1.5 s)^2
Now you can calculate the height of the wall above the water by substituting the values into the equation and solving:
Vertical Displacement (S) = 0.5 × 9.8 m/s^2 × (1.5 s)^2
S = 0.5 × 9.8 m/s^2 × 2.25 s^2
S = 10.9125 m^2/s^2
So, the height of the wall above the water is approximately 10.9 meters.
To find the height of the wall, you can use the equation of motion for horizontal motion:
Distance = Velocity * Time
In this case, the distance is 4.5 m, the velocity is 3.0 m/s, and we need to find the time it takes for the rock to reach the water.
So, rearranging the equation, we have:
Time (T) = Distance / Velocity
T = 4.5 m / 3.0 m/s
T = 1.5 s
Now, to find the height of the wall, we can use the vertical motion equation:
Height = Initial Velocity * Time + (0.5 * Acceleration * Time^2)
Since the boy is throwing the rock horizontally, the initial vertical velocity is 0 m/s, and the acceleration due to gravity is -9.8 m/s^2 (negative because it acts downwards).
Plugging in the values, we have:
Height = (0 * 1.5 s) + (0.5 * -9.8 m/s^2 * (1.5 s)^2)
Height = 0 + (-7.35 m)
Therefore, the height of the wall above the water is -7.35 meters. Note that the negative sign indicates that the height is below the water level.
s=vt
4.5=3t
t=1.5
s=0.5(-10)1.5^2
=-5(1.5)^2
=-11.25 m
The wall is 11.25 m above the water (the answer is negative because the granite falls in a negative direction)