initial velocity?

Question

William tell is shooting at an apple hanging in a tree. The apple is a horizontal distance of 20 m away and at a height of 4 m above the ground. If the arrow is released from a height of 1 m above the ground and hits the apple .5 s later, what is the initial velocity?

Answer 1

equations for this are
y(t)=1+sin(th)*v0*t-.5*g*t^2
and
x(t)=cos(th)*v0*t
when y(.5)=4 and x(.5)=20 we have apple impact.


4=1+sin(th)*vo*.5-.5*9.8*.5^2
20=cos(th)*v0*.5

solve for tan(th) first

8.45=sin(th)*v0

40=cos(th)*v0

tan(th)=8.45/40
th=12 degrees

v0=41 m/s


j

Answer 2

The horizontal velocity of a projectile does not affect how far (or how fast) a projectile falls vertically. Perpendicular components of motion are independent of each other. Thus, an analysis of the motion of a projectile demands that the two components of motion are analyzed independent of each other, being careful not to mix horizontal motion information with vertical motion information. That is, if analyzing the motion to determine the vertical displacement, one would use kinematic equations with vertical motion parameters (initial vertical velocity, final vertical velocity, vertical acceleration) and not horizontal motion parameters (initial horizontal velocity, final horizontal velocity, horizontal acceleration). It is for this reason that one of the initial steps of a projectile motion problem is to determine the components of the initial velocity.

Answer 3

Umm yea what he said ;)