Question

7Unreasonable results A dolphin in an aquatic show jumps straight up out of the water at a velocity of 15.0 m/s.

Answer 1

Answer: See below

Explanation:

a. What is know:

Dolphin's Initial Velocity (Vo) = 15.0 m/s

Gravity Acceleration = 9.8 $m/s^{2}$

We also know that the time the dolphin is in the air it equals to twice the time it takes to reach the highest point on the jump (t).

Total Time (Tt) = 2 * t

b. To choose appropiated equation, we notice that it is know the Dolphin's Initial Velocity  and the gravity. It not know the distance it travels or the time it takes, however, because goes up, it can be know the velocity on the highest point (Vf), which is zero. After reaching this point the Dolphin will fall back again. So it is know:

Vf = 0

Because know we know the final velocity we can calculate the distance traveled to get to that velocity under the gravity des-aceleration, we the following equation:

$Vf^{2} = Vo^{2} + 2 * a *d$

Where the accelaration will be gravity, with a negative sign because it has a diference direction that the velocity, and Vf being 0, simplify the equation. Knowing all the values, we search the distance (d).

$d = \frac{Vo^{2} }{2g}$

Changing the values:

d = 11.46 m

c. To know the time is very easy. Because we know the initial velocity, the gravity and the final velocity. We can use the following equation

$Vf = Vo - gt$

Searching for time we get:

$t = \frac{Vo}{g}$

Which give us a time of: 1.53 s

This is the time it takes to get to the highest point. By doubling it, we know how much it took the dolphin to jump to the highest point and fall back to the water, which is the time it was on air.

Tt = 2 * 1.53 s

Tt= 3.06 s