Question

A projectile is fired horizontally from a cannon atop a 25 m cliff. The projectile has a muzzle velocity of 80 m/s. At what distance from the base of the cliff a target be struck by the projectile? use g = 9.8 m/s²

Answer 1

The target will be struck at a distance of 202.8 m from the base of the cliff.

Step-by-step explanation:

To find the distance from the base of the cliff where the target will be struck, we need to use the equation for horizontal motion of a projectile: d = v * t, where d is the distance, v is the muzzle velocity, and t is the time of flight. In this case, since the projectile is fired horizontally, the vertical component of its velocity is zero, and its time of flight can be found using the equation: t = sqrt((2h) / g), where h is the height of the cliff and g is the acceleration due to gravity.

Given that the muzzle velocity is 80 m/s and the height of the cliff is 25 m, we can calculate the time of flight as follows: t = sqrt((2 * 25) / 9.8) = 2.535 s.

Substituting the values into the equation for horizontal distance: d = 80 * 2.535 = 202.8 m.

Therefore, the target will be struck at a distance of 202.8 m from the base of the cliff.