You throw a ball vertically from an apartment balcony to the ground 14.2 m below. Find the ball's initial velocity if it hits the ground 1.08 s after you release it.
h=vi*t-1/2 9.8 t^2
h=-14.2, solve for vi
To solve this problem, we can use the equations of motion. The equation that relates the initial velocity (v₀), time (t), and displacement (s) is:
s = v₀ * t + (1/2) * g * t²
where g is the acceleration due to gravity (approximately 9.8 m/s²).
In this case, the displacement is given as 14.2 m and the time is given as 1.08 s.
Plugging in these values into the equation, we have:
14.2 = v₀ * 1.08 + (1/2) * 9.8 * (1.08)²
Simplifying the equation, we get:
14.2 = 1.08v₀ + 5.29
Rearranging the equation to solve for v₀, we have:
1.08v₀ = 14.2 - 5.29
1.08v₀ = 8.91
Finally, dividing both sides of the equation by 1.08, we get:
v₀ = 8.91 / 1.08
v₀ ≈ 8.25 m/s
Therefore, the ball's initial velocity is approximately 8.25 m/s.