To find the final velocity (\(V_f\)) of the egg just before it hits the ground, we can use the kinematic equations for uniformly accelerated motion. Since there is no air resistance, the only force acting on the egg is gravity.
The relevant kinematic equation for this scenario is:
\[ V_f^2 = V_i^2 + 2a h \]
Where:
- \( V_f \) is the final velocity
- \( V_i \) is the initial velocity (0 m/s, since the egg is initially at rest)
- \( a \) is the acceleration due to gravity (-9.8 m/s²)
- \( h \) is the height (31.5 m)
Plugging in the known values:
\[ V_f^2 = 0^2 + 2 \times 9.8 \times 31.5 \]
\[ V_f^2 = 2 \times 9.8 \times 31.5 \]
\[ V_f^2 = 19.6 \times 31.5 \]
\[ V_f^2 = 617.4 \]
To find \( V_f \), we take the square root of both sides:
\[ V_f = \sqrt{617.4} \]
\[ V_f \approx 24.84 \text{ m/s} \]
Since we are looking for the downward velocity, and by convention, downward velocities are considered negative vectors:
\[ V_f \approx -24.84 \text{ m/s} \]
So, the final velocity of the egg just before it hits the ground is approximately \( -24.84 \text{ m/s} \).
an egg initially at rest is dropped from the roof of a 31.5m tall building and travels in free fall. What is the final velocity of the egg just before it hits the ground?
Vf=[?] m/s
Do not account for air resistance.
Remember, downward velocity is a negative vector (-).
1 answer
1 answer