A Knight of the Round Table fires off a vat of burning pitch from his catapult at 17.5 m/s, at 36 ◦ above the horizontal. The acceleration of gravity is 9.8 m/s 2 .

Question

1.How long is it in the air? Answer in units of s.

2.What is the horizontal component of the velocity? Answer in units of m/s.

3.How far from the catapult does it land? Answer in units of m.

Answer 1

Hi Nancy K.,

You could probably find formulas around applying to this, and just plug in; but, it's better for you in the long run if you work it through step by step, first.

1) Calculate each of the initial horizontal and initial vertical component velocities, by using trig functions of the initial launch angle. This is usually called "decomposing" the velocity into its vector components.

2) From the initial vertical velocity, calculate the time to apex of trajectory (v(vertical)=0), using v = a*t

What you are doing here is conceptually reframing the problem: moving backwards along the trajectory, from the apex to the launch site, but considering only the vertical component of velocity.

Think of this as just dropping the vat from the apex, to the ground underneath. This is an exact model of what happens to the vertical velocity (only) of the vat during the last 1/2 of its trajectory, since the vertical velocity and the horizontal velocity have nothing at all to do with each other physically -- the vertical is affected by the acceleration of gravity, and the horizontal is constant. And the first 1/2 of the trajectory looks exactly like the second 1/2 in shape and times, just mirror-reversed front/back.

3) This gives you a time for 1/2 of the trajectory travel; double it to get the full trajectory travel time.

4) Use the full time in (3), and the initial horizontal component velocity, to get the full horizontal distance traveled.

If you want to astound your teacher, casually remark that this is exactly like baseball -- first there is the windup (of the catapult), then the (burning!) pitch!

Cheers, -- Mr. d.