Answer:
equation of motion for Bill is
[tex]y(t) = 4.9t^2[/tex]
equation of motion for Ted is
[tex]y(t) = 2 + (-4.2)(t) + 4.9t^2[/tex]
Explanation:
Taking downward position positive and upward position negative
g = 9.8 m/s^2
equation of motion for Bill is
[tex]y(t) = y_0 +v_0 t +\frac{1}{2}gt^2[/tex]
[tex]y(t) = 0 + 0(t) +\frac{1}{2}gt^2[/tex]
[tex]y(t) = \frac{1}{2}\times (9.8t)^2[/tex]
[tex]y(t) = 4.9t^2[/tex]
equation of motion for Ted is
[tex]y_0 = 2m -1m = 2m[/tex]
[tex]y_0 = -4.2 m/s[/tex]
[tex]y(t) = y_0 +v_0 t +\frac{1}{2}gt^2[/tex]
[tex]y(t) = 2 + (-4.2)(t) +\frac{1}{2}gt^2[/tex]
[tex]y(t) = 2 + (-4.2)(t) +\frac{1}{2}\times (9.8t)^2[/tex]
[tex]y(t) = 2 + (-4.2)(t) + 4.9t^2[/tex]
Answer:
Answer:
For Bill:
[tex]x(t)=3-(4.9*t^{2})[/tex]
For Ted:
[tex]x(t)=1+(4.2*t)+(-4.9*t^{2} )[/tex]
Explanation:
For Bill:
[tex]Initial position=x_{0}=3[/tex]
[tex]Initial velocity=v_{0}=0[/tex]
Now using [tex]2^{nd}[/tex] equation of motion,we have
[tex]x-x_{0}=(v_{0} *t)+(1/2*g*t^{2})[/tex]
[tex]x_{0} =3[/tex] ,[tex]v_{0}=0[/tex]
Thus,equation becomes
[tex]x-3=1/2*g*t^{2}[/tex]
[tex]x=3+(0.5*g*t^{2})[/tex]
Taking acceleration upward positive and downward negative.
[tex]g=-10[/tex] [tex]m/s^{2}[/tex]
[tex]x(t)=3-4.9*t^{2}[/tex] for bill
For Ted
[tex]x_{0} =1[/tex]
[tex]v_{0}=4.2[/tex] [tex]m/s[/tex]
Using the same equation
[tex]x-x_{0}=(v_{0} *t)+(1/2*g*t^{2})[/tex]
[tex]x_{0}=1[/tex] [tex]m[/tex]
[tex]v_{0}=4.2[/tex] [tex]m/s[/tex]
Substitute values
[tex]x-1=(4.2*t)+(1/2*g*t^{2})[/tex]
[tex]g=-10[/tex] [tex]m/s^{2}[/tex]
Thus equation becomes
[tex]x(t)=1+(4.2*t)+(-4.9*t^{2})[/tex] for Ted
