Problem 1: An arrow is fired with an initial velocity vo at an angle above horiz
ID: 1516396 • Letter: P
Question
Problem 1: An arrow is fired with an initial velocity vo at an angle above horizontl. Assume the arrow moves without air resistance. Use a Cartesian coordinate system with the origin at the arrow's initial position to analyze the arrow's motion. 0 ©theexpertta.com Part (a) Some time later the arrow makes an angle of = 15 degrees with respect to the horizontal Write an expression for the time, t, that passes between when the arrow was fired and this later point. Final Grade 100% Correct Answer Student Answer t = vo ( sin(80)-cos(80) tan() )/g = ( vo cos(80 ) tan()-v0 sin(80) )/-gExplanation / Answer
Let vertically up be +y direction and right be +x direction
Let the final velocity be v
Horizontal component of velocity will not change.
so,
vo*cos thetha0 =v*cos thetha
v= (vo*cos thetha0)/cos thetha
vertical component:
vi = vo*sin thetha
vf = v*sin thetha
= sin thetha * (vo*cos thetha0)/cos thetha
= (vo*cos thetha0) * tan thetha
a = -g m/s^2
use;
vf = vi + a*t
(vo*cos thetha0) * tan thetha = vo*sin thetha - g*t
gt = vo*sin thetha - (vo*cos thetha0) * tan thetha
t = {vo*sin thetha - (vo*cos thetha0) * tan thetha } / g