Question

An archer stands at rest on 5 frictionless ice; his total mass including his bow and quiver of arrows is 65.00 kg. He then fires a 0.030 O-kg arrow at 50.0 m/s at an angle of 30.0° above the horizontal. If it takes 650N of force to break the ice and the arrow leaves the bow in 10ms, does the archer fall into the frozen lake?​

Answer 1

The impulse allows finding the result for the force that the arrow exerts on the ice is:

• The force of the arrow (75N) is much less than the force necessary to break the ice (650N), therefore the archer does not fall into the frozen lake.

The impulse is the force per time on a given surface, we use the relationship between the impluse and the momentum.

     I = ∫F  dt = Δp

where I is the impulse, F the force, t the time and p the momentum.

In the attachment we can see a free body diagram of the system, in the vertical axis (y) the amount of movement is indicated.

The force to break the ice is vertical, let's look for the impulse on this axis.

y-axis

      $F_y t = p_f - p_o$

Before releasing the arrow its speed is zero.

      $F_y = \frac{m v_y}{t}$  

     

Let's use trigonometry to find the vertical component of the velocity.

    sin 30 = $\frac{v_y}{v}$  

    $v_y$ = v sin30

Let's substitute.

    $F_y = \frac{m v \ sin 30}{t}$  

Let's calculate.

      $F_y = \frac{0030 \ 50.0 \ sin 30}{10 \ 10^{-3}}$  

      Fy = 75 N

We can see that the force of the arrow on the ice is much less than the force necessary to break the ice therefore the archer does not fall into the lake.

Learn more here: brainly.com/question/904448