Question

1. chintu and raven build a rocket, which moves from the earth to about 86m into the sky. it takes 3.7 seconds to reach the rockets highest point. what is his speed of the rockets ascent?

Explanation:

Step1: Identify the kinematic - equation

We use the kinematic equation $x = v_0t+\frac{1}{2}at^2$. At the highest - point, the final velocity $v = v_0+at = 0$, and the acceleration $a=-g=- 9.8m/s^2$ (taking upward as positive and acceleration due to gravity acts downward). Also, the initial velocity $v_0$ is what we want to find, and the displacement $x = 86m$, time $t = 3.7s$, and $a=-9.8m/s^2$.
We can also use the equation $x=v_0t-\frac{1}{2}gt^2$.

Step2: Rearrange the equation to solve for $v_0$

From $x = v_0t-\frac{1}{2}gt^2$, we can solve for $v_0$.
\[v_0=\frac{x+\frac{1}{2}gt^2}{t}\]
Substitute $x = 86m$, $g = 9.8m/s^2$, and $t = 3.7s$ into the formula.
\[v_0=\frac{86+\frac{1}{2}\times9.8\times(3.7)^2}{3.7}\]
\[v_0=\frac{86 + \frac{1}{2}\times9.8\times13.69}{3.7}=\frac{86+67.181}{3.7}=\frac{153.181}{3.7}\approx41.4m/s\]

Answer:

The speed of the rocket's ascent is approximately $41.4m/s$.