A hunter aims his gun and fires a bullet directly at a monkey. At the instant the bullet is fired, the monkey drops. The minimum speed for the bullet to hit monkey is..?
the minimum speed must be greater than accelertion due to gravity..............but to tell exactly we need the distance between the hunter and monkey
To determine the minimum speed required for the bullet to hit the monkey, let's analyze the motion of both the bullet and the monkey.
Assuming there is no air resistance, the bullet would travel in a straight line at a constant speed. On the other hand, the monkey would start accelerating downward due to the force of gravity.
We can use the kinematic equations to analyze the vertical motion of the monkey. The equation that relates the displacement (Δy), initial velocity (v₀), time (t), and acceleration (a) is:
Δy = v₀t + (1/2)at²
Since the monkey drops as soon as the bullet is fired, we can assume that the time taken for the bullet to reach the monkey is negligible. Therefore, the time (t) in the equation is considered to be zero.
We know that the monkey's displacement (Δy) is equal to zero when it drops. The initial velocity (v₀) of the monkey is also zero since it is at rest. Thus, the equation simplifies to:
0 = (1/2)at²
Since the acceleration due to gravity (a) is approximately 9.8 m/s², we can substitute the value in the equation:
0 = (1/2)(9.8)t²
Simplifying further:
0 = 4.9t²
This equation tells us that t = 0 (an instant after the bullet is fired) is a valid solution.
Therefore, at the instant the bullet is fired, the monkey starts falling without having traveled any distance horizontally. This means that the bullet, to hit the monkey, needs to reach horizontally from the gun to the monkey before it falls.
In conclusion, the minimum speed for the bullet to hit the monkey is dependent on the horizontal distance between the hunter and the monkey, rather than the vertical motion or acceleration.