Question

Howard is the first human who step foot on Planet Funkatron. His first is to determine the force due to gravity,which notice to be quite different the force due to gravity on Earth. His first test is quite simple:he pick up a rock and throws it in the air from initial height y=1.5m with initial velocity v0=29.5m\s i+3.35m\s j .To his surprise the rock return to same point from which it was thrown 5.25sec later.

Can you find free body diagram and acceleration due to gravity?

Answer 1

V = Vi i + Vj j
so unit vector in direction of Vu = \[Vi/\sqrt{Vi^2 + Vj^2} i + Vj/\sqrt{Vi^2 + Vj^2} j\]
now acceleration should have the same unit vector, then the rock can return back to the same point
hence acceleration is of the form,
\[A = Ao* (Vi/\sqrt{Vi^2 + Vj^2} i + Vj/\sqrt{Vi^2 + Vj^2} j\]

now, the object was thrown in the same direction as the acceleration vector.
so, we can simply say, time taken t = 2*initial velocity magnitude/acceleration magnitude
t = 2 * Vo/Ao

\[Vo = \sqrt{Vi^2 + Vj^2}\] = \[\sqrt{29.5^2 + 3.35^2}\] = 29.69

hence, Ao = 2*Vo/t = 2 * 29.69 / 5.25 = 11.31

hence \[A = 11.31 * (29.5/29.69 i + 3.35/29.69 j )\]
A = 11.24 i + 1.28 j

Answer 2

You awesome man.