<jupyter_start><jupyter_text>$h=h_{\circ}+v_{\circ}t-\frac{1}{2}gt^{2}$ $v=v_{\circ}-gt$ $g=9.8 m/s^{2}$ $h_{\circ}=1.6m$ $v_{\circ}=14.2m/s$ (i) velocity and height after $t=0.5s $ (ii)velocity and height after $t=2.0s $<jupyter_code>import numpy as np
h0=1.6
v0=14.2
g=9.8
def f(t):
    return h0+v0*t-1/2*g*t**2
print(f(0.5))
print(f(2.0))<jupyter_output>10.399999999999999<jupyter_text>$v=v_{\circ}(1-\frac{z}{\sqrt(a^{2}+z^{2})})$<jupyter_code>v0=10
a=2.5
def f(z):
    return v0*(1-z/np.sqrt(a**2+z**2))
print(f(4.33))
print(f(8.25))<jupyter_output>0.42975595566526414<jupyter_text>Alternate Method<jupyter_code>v0=10
a=2.5
z=4.33
f=v0*(1-z/np.sqrt(a**2+z**2))
print(f)
h0=1.6
v0=14.2
g=9.8
t=0.5
x=h0+v0*t-1/2*g*t**2
print(x)<jupyter_output>7.475
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