Question

1. upton chuck is riding the giant drop at great america. if upton free - falls for 2.60 seconds, what will be his final velocity and how far will he fall?
2. a race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. determine the acceleration of the car and the distance traveled.

Explanation:

Problem 3

Step1: Find final velocity

Use the formula $v = v_0+at$. In free - fall, $v_0 = 0$ (starts from rest), $a = g= 9.8\ m/s^2$ and $t = 2.60\ s$.
$v=0 + 9.8\times2.60$
$v = 25.48\ m/s$

Step2: Find distance fallen

Use the formula $d=v_0t+\frac{1}{2}at^2$. Since $v_0 = 0$, the formula simplifies to $d=\frac{1}{2}at^2$.
$d=\frac{1}{2}\times9.8\times(2.60)^2$
$d = 33.124\ m$

Step1: Determine acceleration

Use the formula $a=\frac{v - v_0}{t}$, where $v_0 = 18.5\ m/s$, $v = 46.1\ m/s$ and $t = 2.47\ s$.
$a=\frac{46.1 - 18.5}{2.47}$
$a=\frac{27.6}{2.47}\approx11.17\ m/s^2$

Step2: Determine distance traveled

Use the formula $d=v_0t+\frac{1}{2}at^2$. Substitute $v_0 = 18.5\ m/s$, $a\approx11.17\ m/s^2$ and $t = 2.47\ s$.
$d=18.5\times2.47+\frac{1}{2}\times11.17\times(2.47)^2$
$d = 18.5\times2.47+ \frac{1}{2}\times11.17\times6.1009$
$d = 45.695+34.039$
$d\approx79.73\ m$

Answer:

Final velocity: $25.48\ m/s$, Distance fallen: $33.124\ m$

Problem 4