The time of flight is 15.0 s
Explanation:
The motion of the arrow is the motion of a projectile, which consists of two separate motions:
- A uniform motion along the horizontal direction, with constant velocity
- A uniformly accelerated motion along the vertical direction, with constant acceleration [tex]g=9.8 m/s^2[/tex] towards the ground
From the equations of motion along the two dimensions, it is possible to find an expression for the time of flight of a projectile. In fact, we can use the following suvat equation for the vertical motion:
[tex]v_y = u_y -gt[/tex]
where
[tex]v_y[/tex] is the vertical velocity at time t
[tex]u_y = u sin \theta[/tex] is the initial vertical velocity, with
u = 83.0 m/s being the initial speed
[tex]\theta=62.0^{\circ}[/tex] being the angle of projection
The arrow reaches its maximum altitude when the vertical velocity becomes zero, so when
[tex]v_y = 0[/tex]
Which means that the equation becomes
[tex]0=u sin \theta - gt[/tex]
So, the time to reach the maximum altitude is
[tex]t=\frac{u sin \theta}{g}[/tex]
The time of flight is just twice the time needed to reach the maximum altitude, so:
[tex]T=2t=\frac{2u sin \theta}{g}[/tex]
And substituting the data for this arrow, we find:
[tex]T=\frac{2(83.0)(sin 62.0^{\circ})}{9.8}=15.0 s[/tex]
Learn more about projectile motion:
brainly.com/question/8751410
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