Question

a cannonball is launched horizontally with an initial velocity of 50 m/s off a 100 m tall cliff. the goal is to have the cannonball travel a target range of 150 m (within a few meters). based on the information provided, will the cannonball reach the target distance? a more information is needed to determine the outcome b no, the cannonball will overshoot its goal c no, the cannonball will fall short of the goal d yes, the cannonball will hit its goal

Explanation:

Step1: Calculate time of fall

The vertical - motion of the cannonball is a free - fall. The height of the cliff $h = 100$ m, and the initial vertical velocity $v_{0y}=0$ m/s. Using the equation $h = v_{0y}t+\frac{1}{2}gt^{2}$, since $v_{0y} = 0$ m/s, we have $h=\frac{1}{2}gt^{2}$. Solving for $t$, we get $t=\sqrt{\frac{2h}{g}}$. Substituting $h = 100$ m and $g = 9.8$ m/s², $t=\sqrt{\frac{2\times100}{9.8}}\approx\sqrt{20.41}\approx4.52$ s.

Step2: Calculate horizontal distance

The horizontal velocity $v_{x}=50$ m/s is constant (no horizontal acceleration in the absence of air - resistance). Using the equation $x = v_{x}t$, substituting $v_{x}=50$ m/s and $t = 4.52$ s, we get $x=50\times4.52 = 226$ m.

Step3: Compare with target distance

The target distance is 150 m. Since $226$ m$>150$ m, the cannonball will overshoot its goal.

Answer:

B. no, the cannonball will overshoot its goal