Question

1. you do: if you were to throw a large log over the edge of the grand canyon and it took 5.65 seconds to hit the ground, calculate the velocity of the log at impact in m/s. 56.5m/s 5. you do: now calculate the distance the log fell. 6. you do: mr. martinek is at a punk show and is getting very into the music. he climbs up the speakers on the side of the stage and dives off into the crowd, who carry him to the exit and promptly dump him in the parking lot. if he was able to calculate that he was traveling at 7.8 m/s upon being caught, how high off the ground was the speaker he jumped off of? 7. you do: how long did it take him to reach the end of his stage dive?

Explanation:

4.

Step1: Use free - fall velocity formula

The formula for the final velocity $v$ in free - fall is $v = v_0+gt$, where the initial vertical velocity $v_0 = 0$ (thrown horizontally or just dropped), $g = 9.8\ m/s^2$ (acceleration due to gravity) and $t$ is the time of fall.
$v=0 + gt$

Step2: Substitute values

Given $t = 5.65\ s$ and $g=9.8\ m/s^2$, we substitute into the formula:
$v=9.8\times5.65$
$v = 55.37\ m/s$ (There might be a rounding difference in the provided answer of 56.5 m/s)

5.

Step1: Use free - fall distance formula

The formula for the distance $d$ an object falls in free - fall is $d=v_0t+\frac{1}{2}gt^{2}$, with $v_0 = 0$ (assuming no initial vertical velocity).
$d=\frac{1}{2}gt^{2}$

Step2: Substitute values

Given $t = 5.65\ s$ and $g = 9.8\ m/s^2$, we have:
$d=\frac{1}{2}\times9.8\times(5.65)^{2}$
$d = 4.9\times31.9225$
$d=156.42025\ m$

6.

Step1: Use conservation of mechanical energy

The kinetic energy $K=\frac{1}{2}mv^{2}$ when caught is equal to the potential energy $U = mgh$ at the height $h$ of the speaker. Since $K = U$, we have $\frac{1}{2}mv^{2}=mgh$. Canceling out the mass $m$ on both sides, we get $h=\frac{v^{2}}{2g}$.

Step2: Substitute values

Given $v = 7.8\ m/s$ and $g = 9.8\ m/s^2$, we substitute:
$h=\frac{(7.8)^{2}}{2\times9.8}$
$h=\frac{60.84}{19.6}$
$h\approx3.1\ m$

7.

Answer:

Step1: Use free - fall velocity formula to find time

We know $v = v_0+gt$, with $v_0 = 0$ (no initial vertical velocity) and $v$ is the velocity when caught. So $t=\frac{v - v_0}{g}$.

Step2: Substitute values

Given $v = 7.8\ m/s$ and $v_0 = 0$, $g = 9.8\ m/s^2$
$t=\frac{7.8-0}{9.8}$
$t\approx0.8\ s$