Answer:
a) Time = 2.67 s
b) Height = 35.0 m
Explanation:
a) The time of flight can be found using the following equation:
[tex] x_{f} = x_{0} + v_{0_{x}}t + \frac{1}{2}at^{2} [/tex] (1)
Where:
[tex] x_{f}[/tex]: is the final position in the horizontal direction = 80 m
[tex] x_{0}[/tex]: is the initial position in the horizontal direction = 0
[tex]v_{0_{x}}[/tex]: is the initial velocity in the horizontal direction = 30 m/s
a: is the acceleration in the horizontal direction = 0 (the stone is only accelerated by gravity)
t: is the time =?
By entering the above values into equation (1) and solving for "t", we can find the time of flight of the stone:
[tex] t = \frac{x_{f}}{v_{0}} = \frac{80 m}{30 m/s} = 2.67 s [/tex]
b) The height of the hill is given by:
[tex] y_{f} = y_{0} + v_{0_{y}}t - \frac{1}{2}gt^{2} [/tex]
Where:
[tex] y_{f}[/tex]: is the final position in the vertical direction = 0
[tex] y_{0}[/tex]: is the initial position in the vertical direction =?
[tex]v_{0_{y}}[/tex]: is the initial velocity in the vertical direction =0 (the stone is thrown horizontally)
g: is the acceleration due to gravity = 9.81 m/s²
Hence, the height of the hill is:
[tex] y_{0} = \frac{1}{2}gt^{2} = \frac{1}{2}9.81 m/s^{2}*(2.67 s)^{2} = 35.0 m [/tex]
I hope it helps you!
