Final answer:
To find the muzzle velocity of a bullet aimed at a squirrel, we must consider both horizontal and vertical motion. The horizontal velocity is calculated based on the distance to the squirrel over the time of flight. As there's no vertical displacement, the muzzle velocity is equal to the horizontal component, which is 41.67 m/s.
Step-by-step explanation:
To calculate the muzzle velocity of the bullet in this scenario, we need to consider the horizontal and vertical components of the projectile's motion separately. The horizontal component involves the distance to the squirrel, and the vertical component involves the height of the squirrel up the tree.
Firstly, we can calculate the horizontal component of velocity using the formula ℓ = d / t, where ℓ is the horizontal velocity, d is the distance to the target (25 m), and t is the time of flight (0.6 s). This gives us ℓ = 25 m / 0.6 s = 41.67 m/s.
Secondly, the vertical component of velocity, ℓy, must be found by considering the effects of gravity. Since the squirrel is at the same height as the gun, there's no initial vertical velocity, so we can use the formula s = ½ g t², where s is the vertical displacement (12.5 m), and g is the acceleration due to gravity (9.8 m/s²). However, as the vertical position of the squirrel in the tree doesn't change, the initial vertical velocity component (ℓy) is 0, and thus the muzzle velocity is the same as the horizontal component.
Therefore, the muzzle velocity of the bullet is 41.67 m/s.