Question

You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 68.0 m away, making a 3.00o angle with the ground. How fast was the arrow shot?

Answer 1

Answer:112.82 m/s

Explanation:

Given

range of arrow=68 m

$Angle=3^{\circ}$

as the arrow travels it acquire a vertical velocity $v_y$

$v_y=u+at$

$v_y=0+9.81\times t$-------1

Range is given by

R=ut

where u=initial velocity

$68=u\times t$

$t=\frac{68}{u}$

substitute the value of t in eqn 1

$v_y=9.81\times \frac{68}{u}$

$v_y\times u=9.81\times 68=667.08$--------2

and $tan(3)=\frac{v_y}{u}$

$v_y=utan(3)=0.0524u$

substitute it in 2

$0.0524 u^2=667.08$

$u^2=12,728.644$

u=112.82 m/s

Answer 2

Velocity of a object is the ratio of distance traveled by the object with the time taken. The speed of the arrow shot is 112.83 m/s.

What is velocity of a object?

Velocity of a object is the ratio of distance traveled by the object with the time taken.

Given information-

The arrow stuck in the ground 68.0 m away.

The angle made by the arrow with the ground is 3 degrees.

Convert this angle into the radians as,

$\theta=\dfrac{\pi}{180}\times3 \\\theta=0.0524 \rm rad$

Thus, the angle made by the arrow with the ground is 0.0524 radians.

The ratio of the vertical velocity $v_y$ and the horizontal velocity $v_x$ is,

$tan\theta=\dfrac{v_y}{v_x}=\theta \rm (for \;smaller \;angle)$

Put the values as,

$\dfrac{v_y}{v_x}=0.0524\\v_y=0.0524v_x$          .....1

Let the above equation as equation 1.

Time taken by the arrow to traveled the distance of 68 meters with horizontal velocity is,

$t=\dfrac{68}{v_x}$

Now the vertical velocity can be given as,

$v_y=gt$

Put the value of vertical velocity from equation 1 and the value of time in the above equation as,

$0.0524v_x=9.81\times\dfrac{68}{v_x}\\v_x=112.83\rm m/s$

Thus, the speed of the arrow shot is 112.83 m/s.

Learn more about the velocity here;

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