Question

A potato cannon is fired at an angle of 42.0o . If the potato leaves the cannon at a velocity of 62.3 m/s, calculate the range of the potato.

Answer 1

Let's first find the time that the potato takes to reach the maximum height:

$$v_y=v_0sin\theta-gt_{rise},$$ $$0=v_0sin\theta-gt_{rise},$$ $$t_{rise}=\dfrac{v_0sin\theta}{g}=\dfrac{62.3\ \dfrac{m}{s}\cdot sin42^{\circ}}{9.8\ \dfrac{m}{s^2}}=4.25\ s.$$

Then, we can find the total time of flight of the potato:

$$t=2t_{rise}=2\cdot 4.25\ s=8.5\ s.$$

Finally, we can find the range of the potato from the kinematic equation:

$$x=v_0tcos\theta=62.3\ \dfrac{m}{s}\cdot 8.5\ s\cdot cos42^{\circ}=393.5\ m.$$

Answer:

$x=393.5\ m.$