Answer:
For Bill to dump the water on Tim, Tim should be 7.232 meters from the tree when Bill dumps the water
Explanation:
The given height above the ground at which Bill sits on the tree branch with a bucket of water, h = 4.0 meters
The speed with which Tim is approaching the tree = 8.0 meters per second
The time , t, it will take for the bucket of water to reach the ground is given by the equation of free fall as follows;
h = 1/2·g·t²
Where;
h = Height = 4.0 m
g = The acceleration due to gravity ≈ 9.8 m/s²
t = The time
Making t the subject of the above equation gives;
t = √(h/(1/2·g))
Substituting the known values gives;
t = √(4.0 m/(1/2 × 9.8 m/s²)) ≈ 0.904 s
t ≈ 0.904 seconds
Therefore, for Bill to dump the water on Tim, it should take Tim approximately 0.904 seconds to get to the tree
The distance, d, Tim will be when it will take him 0.904 seconds to get to the tree is given from the kinematic equation of speed, s, as follows;
Distance, d = Time, t × Speed, s
Where;
d = The distance
t = The time = 0.904 s
s = The speed with which Tim is approaching the tree = 8.0 m/s
Substituting the values gives;
d = 0.904 s × 8.0 m/s = 7.232 m
Therefore, the distance Tim should be when Bill throws the water = 7.232 meters
