If you jump upward with a speed of 1.7 m/s, how high will you be when you stop rising?

Vf^2 = Vo^2 + 2ad,

d = (Vf^2 - Vo^2) / 2g,
d(up) = (0 - (1.7)^2) / -19.6 = 0.15m.

To determine the height when you stop rising after jumping upward with a speed of 1.7 m/s, we can use the principles of motion and the equations of motion.

The equation we need to use is the kinematic equation for vertical motion:

vf^2 = vi^2 + 2ad

Where:
vf = final velocity (which will be zero when you stop rising)
vi = initial velocity (1.7 m/s in this case)
a = acceleration (which is equal to the acceleration due to gravity, approximated as -9.8 m/s^2)
d = displacement or height (what we want to find)

Rearranging the equation, we can solve for d:

0^2 = (1.7 m/s)^2 + 2 * (-9.8 m/s^2) * d

0 = 2.89 m^2/s^2 - 19.6 m/s^2 * d

-2.89 m^2/s^2 = -19.6 m/s^2 * d

d = -2.89 m^2/s^2 / -19.6 m/s^2

d ≈ 0.147 m

So, when you stop rising, you will be approximately 0.147 meters high.

To find out how high you will be when you stop rising after jumping upward with a speed of 1.7 m/s, we can use the principles of projectile motion.

Step 1: Determine the initial vertical velocity (v₀y):
In this case, the initial vertical velocity is the speed at which you jump upward, which is 1.7 m/s. Since we are considering upward motion only, the initial vertical velocity is positive.

Step 2: Determine the acceleration in the vertical direction (aₙ):
The acceleration due to gravity (g) acts in the downward direction and its value is approximately 9.8 m/s².

Step 3: Use the kinematic equation to solve for the height (h):
The kinematic equation that relates the final velocity (v_y) in the vertical direction, the initial vertical velocity (v₀y), the acceleration in the vertical direction (aₙ), and the height (h) is:
v_y² = v₀y² + 2aₙh

Since you want to find the height when you stop rising, your final vertical velocity (v_y) will be zero. Thus, the equation becomes:
0 = v₀y² + 2aₙh

Now we can substitute the known values into the equation:
0 = (1.7 m/s)² + 2(-9.8 m/s²)h

Simplifying the equation:
0 = 2.89 m²/s² - 19.6 m/s²h

Rearranging the equation to solve for h:
19.6 m/s²h = 2.89 m²/s²
h = 2.89 m²/s² / 19.6 m/s²
h ≈ 0.1477 m

Therefore, when you stop rising, you will be approximately 0.1477 meters (or 14.77 centimeters) above your initial position.