An archer fires an arrow at a velocity of #40# #ms^-1# and an angle of #45^o# to the horizontal, from a point #1.5# #m# above the ground. Will the arrow reach a tree #400# #m# from the archer?
1 Answer
The arrow will travel a little more than
Explanation:
First find the two components of the initial velocity:
The horizontal velocity will remain constant, the vertical velocity will change due to the acceleration due to gravity.
In the vertical direction:
The vertical component of the velocity will decrease to
#y=(v_y-u_y)/a_y=(0-28.3)/(-9.8)=2.9 s.
The acceleration due to gravity takes a negative sign because it is in the opposite direction to the initial velocity.
The total time of flight will be twice this, so
The horizontal distance traveled in this time will be given by
This is the distance traveled by the time the arrow returns to the level at which it was released,