Question

Julietta and Jackson are playing miniature golf. Julietta's ball rolls into a long. Straight upward incline with a speed of 2.95 m/s and accelerates at -0.876 m/s/s for 1.54 seconds until it reaches the top of the incline and then continues along an elevated section. Determine the length of the incline.

Answer 1

Answer:

The length of the incline is 3.504 meters.

Explanation:

Let suppose that Julietta's ball decelerates uniformly, then we determine the length of the incline is determined by the following equation of motion:

$\Delta s = v_{o}\cdot t +\frac{1}{2}\cdot a \cdot t^{2}$ (Eq. 1)

Where:

$\Delta s$ - Length of the incline, measured in meters.

$v_{o}$ - Initial speed of the ball, measured in meters per second.

$a$ - Aceleration of the ball, measured in meters per square second.

$t$ - Time, measured in second.

If we know that $v_{o} = 2.95\,\frac{m}{s}$, $t = 1.54\,s$ and $a = -0.876\,\frac{m}{s^{2}}$, then the length of the incline is:

$\Delta s = \left(2.95\,\frac{m}{s} \right)\cdot (1.54\,s)+\frac{1}{2}\cdot \left(-0.876\,\frac{m}{s^{2}} \right) \cdot (1.54\,s)^{2}$

$\Delta s = 3.504\,m$

The length of the incline is 3.504 meters.