A hunter at a distance dx from a coconut tree points the nuzzle of his gun directly at a monkey sitting on the tree at a height dy. The monkey sees the hunters and drops vertically from the tree at the very instant of firing. Will it be hit by the bullet?
Yes. Both the bullet and the monkey accelerate down at 9.8 m/s^2
To determine whether the monkey will be hit by the bullet, we need to consider the time it takes for the bullet to reach the tree and the time it takes for the monkey to reach the ground.
First, let's break down the problem into its components. We have the horizontal distance between the hunter and the coconut tree (dx) and the vertical height of the tree (dy).
The time it takes for the bullet to reach the tree can be calculated using the horizontal distance dx. Assuming the bullet travels at a constant speed, we can use the formula:
time = distance / speed
Now, let's consider the time it takes for the monkey to reach the ground after dropping from the tree. The vertical distance the monkey falls is dy. We can calculate the time using the formula for free fall:
time = sqrt((2 * distance) / acceleration)
Where acceleration is the acceleration due to gravity, approximately 9.8 m/s^2.
If the time it takes for the bullet to reach the tree is greater than the time it takes for the monkey to reach the ground, then the bullet will hit the monkey. Otherwise, the monkey will not be hit.
To summarize, calculate the time it takes for the bullet to reach the tree using dx and the speed of the bullet. Then calculate the time it takes for the monkey to reach the ground using dy and the acceleration due to gravity. Compare these two calculated times to determine if the bullet will hit the monkey.