Question

A soccer ball is released from rest at the top of a grassy incline. After 2.2 seconds, the ball travels 22 meters. One second later, the ball reaches the bottom of the incline. (Assume that the acceleration was constant.) How long was the incline

Answer 1

x = 46.54m

Step-by-step explanation:

In order to find the length of the incline you use the following formula:

`x=v_ot+(1)/(2)at^2` (1)

vo: initial speed of the soccer ball = 0 m/s

t: time

a: acceleration

You first use the the fact that the ball traveled 22 m in 2.2 s. Whit this information you can calculate the acceleration a from the equation (1):

`22m=(1)/(2)a(2.2s)^2\\\\a=9.09(m)/(s^2)` (2)

Next, you calculate the distance traveled by the ball for t = 3.2 s (one second later respect to t = 2.2s). The values of the distance calculated is the lenght of the incline:

`x=(1)/(2)(9.09m/s^2)(3.2s)^2=46.54m` (3)

The length of the incline is 46.54 m