What is its initial vertical speed? The acceleration of gravity is 9.8 m/s
2
and maximum
height is 4.7 m ,. Neglect air resistance.
Answer in units of m/s
124.56
To determine the initial vertical speed, we can use the equations of motion for vertical motion. In this case, we are given that the acceleration due to gravity is 9.8 m/s² and the maximum height is 4.7 m. We need to find the initial vertical speed.
The equation that relates the final velocity (vf), initial velocity (vi), acceleration (a), and displacement (d) is:
vf² = vi² + 2ad
In this case, since the object is at the maximum height, the final velocity is 0 m/s. The displacement, d, is the maximum height, which is 4.7 m. And the acceleration, a, is equal to the acceleration due to gravity, which is -9.8 m/s² (taking the negative sign because gravity acts in the opposite direction).
Plugging in the known values into the equation, we have:
0 = vi² + 2(-9.8)(4.7)
Simplifying the equation, we get:
-2(9.8)(4.7) = vi²
-92.12 = vi²
To solve for vi, we take the square root of both sides:
vi ≈ ±9.60 m/s
Since velocity is a vector quantity with direction, we include both positive and negative values. However, in this case, we are interested in the initial vertical speed, which is the speed at which the object is moving upwards. Therefore, the initial vertical speed is approximately 9.60 m/s (positive value).
So, the initial vertical speed is approximately 9.60 m/s.