Question

Help asap please

1. During a medieval siege of a castle, the attacking army uses a trebuchet to hurl heavy stones at the castle walls. If the trebuchet launches the stones with a velocity of +35.0 m/s at an angle of 60.0°, how long does it take the stone to hit the ground? What is the maximum distance that the trebuchet can be from the castle wall to be in range? How high will the stones go? Show all your work.

Answer 1

How long does it take the stone to hit the ground? Well you have an initial velocity u and a negative acceleration due to gravity g. You want to know when it reaches 0 distance (the ground) again.
Solve this equation
\[ut - \frac{1}{2}gt^2 = 0\]
for t, where
\[u = 35\text{ ms}^{-1} \times \sin60^\circ; g = 9.81\text{ ms}^{-1}\]
Since it's quadratic in t, there will be two solutions. One is zero, the other is the answer.

Maximum distance. Simply the horizontal velocity times the time of flight.
\[d = 35\text{ ms}^{-1} \times \cos60^\circ \times t\]
where t is what you've just worked out.

How high will the stones go? You want the distance at half the flight time.

\[h = u\frac{t}{2} - \frac{1}{2}g\Big(\frac{t}{2}\Big)^2\]

where u, g, t have the same meanings as before.