Question

A historical society is testing an old cannon. They

Answer 1

Answer:

26.2 m/s

Explanation:

We can find the speed of the cannonball just by analyzing its vertical motion. In fact, the initial vertical velocity is

$u_y = u sin \theta$ (1)

where u is the initial speed and $\theta = 45.0^{\circ}$ is the angle of projection.

We can therefore use the following suvat equation for the vertical motion of the ball:

$v_y = u_y + at$

where $v_y$ is the vertical velocity at time t, and $a=g=-9.8 m/s^2$ is the acceleration of gravity. The time of flight is 3.78 s, so we know that the ball reaches its maximum height at half this time:

$t=\frac{3.78}{2}=1.89 s$

And at the maximum height, the vertical velocity is zero:

$v_y=0$

Substituting these values, we find the initial vertical velocity:

$u_y = v_y - at = 0-(-9.8)(1.89)=18.5 m/s$

And using eq.(1) we now find the initial speed:

$u=\frac{u_y}{sin \theta}=\frac{18.5}{sin 45.0^{\circ}}=26.2 m/s$