⚙ Meccanica

A cannon is placed on top of a cliff $h = 80\,\mathrm{m}$ above sea level. The cannon fires a projectile with initial speed $v_0 = 50\,\mathrm{m/s}$ at an angle $\theta = 30°$ above the horizontal. Determine: (a) the total time of flight, (b) the range (horizontal distance from the base of the cliff), (c) the velocity (magnitude and direction) at impact with the water.

Two cars A and B start on the same straight line. Car A starts from rest ($v_{A0} = 0$) with constant acceleration $a_A = 3\,\mathrm{m/s^2}$. Car B already has speed $v_{B0} = 10\,\mathrm{m/s}$ and accelerates with $a_B = 1.5\,\mathrm{m/s^2}$. Both start from the same point ($x=0$) at the same time ($t=0$). Determine: (a) after how long A catches B, (b) at what distance from the start the overtaking occurs, (c) the relative velocity of A with respect to B at the overtaking instant.

A boat crosses a river $d = 120\,\mathrm{m}$ wide. The boat speed relative to the water is $v_b = 4\,\mathrm{m/s}$, while the river current flows parallel to the bank at $v_f = 3\,\mathrm{m/s}$. (a) If the boat points perpendicular to the bank, how long does it take to cross and how far downstream is it carried? (b) At what angle relative to the perpendicular must the boat point to arrive exactly opposite the starting point (zero drift)?