Question

1. a rock dropped from the top of a cliff picks up speed as it falls. both speed and distance are zero at time ( t = 0 ) seconds as shown on the speedometer and odometer. note that after falling 1 second, the speed reading is ( 10 , \text{m/s} ) and the distance dropped is 5 meters. what is the rocks speed and distance at time ( t = 3 ) seconds? use ( g = 10 , \text{m/s}^2 ) and ignore air resistance.

Explanation:

Step1: Calcular la velocidad

La ecuación para la velocidad en caída libre es \(v = gt\). Dado \(g = 10\ m/s^{2}\) y \(t = 3\ s\), entonces \(v=10\times3 = 30\ m/s\).

Step2: Calcular la distancia

La ecuación para la distancia en caída libre es \(d=\frac{1}{2}gt^{2}\). Sustituyendo \(g = 10\ m/s^{2}\) y \(t = 3\ s\), \(d=\frac{1}{2}\times10\times3^{2}=\frac{1}{2}\times10\times9 = 45\ m\).

Answer:

Speed = 30 m/s ; Distance = 45 meters