Answer:
- Yes
- t = x/v0v
Explanation:
Let v0h and v0v represent the horizontal and vertical speeds of the bullet, respectively. Let x represent the distance from the hunter to the tree, and t represent time. h is defined as in the problem statement.
In order for the bullet to be aimed at the initial position of the monkey, (x, h), we must have v0v/v0h = h/x. This means ...
v0h = (x/h)v0v
The time it takes for the bullet to reach the horizontal position of the tree is ...
time = distance/speed
t1 = x/v0h = x/(x·v0v/h)
t1 = h/v0v
The vertical position of the bullet is given by
hb(t) = v0v·t -(1/2)gt^2
When the bullet reaches the horizontal position of the tree, that height is ...
hb(t1) = v0v·t1 -(1/2)g·t1^2
hb(t1) = h -(1/2)g·t1^2
The vertical position of the monkey is given by
hm(t) = h -(1/2)gt^2
so, at t1, the height of the monkey is ...
hm(t1) = h -(1/2)g·t1^2
Comparing the expressions for the height of the monkey and the height of the bullet at the time the bullet reaches the horizontal position of the tree, we find they are identical. That is, the bullet and the monkey occupy the same space. We presume the monkey is killed at time t1 = h/v0v.