Respuesta :
Answer:
A) 3.11 seconds
B) 82.33 m
C) 5.32 seconds
D) 25.2 m/s
Explanation:
t = Time taken
u = Initial velocity = 12 m/s
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s²
[tex]v=u+at\\\Rightarrow 0=12-9.8\times t\\\Rightarrow \frac{-12}{-9.81}=t\\\Rightarrow t=1.22 \s[/tex]
Time taken to reach maximum height is 1.22 seconds
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=12\times 1.22+\frac{1}{2}\times -9.81\times 1.22^2\\\Rightarrow s=7.33\ m[/tex]
So, the stone would travel 7.33 m up
B) So, total height stone would fall is 7.33+75 = 82.33 m
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 82.33=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{82.33\times 2}{9.81}}\\\Rightarrow t=4.1\ s[/tex]
A) Total time taken by the stone to reach the ground from the time it left the person's hand is 4.1+1.22 = 5.32 seconds.
C) When s = 82.33-50 = 33.33 m
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 32.33=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{32.33\times 2}{9.81}}\\\Rightarrow t=2.57\ s[/tex]
The time it takes from the person's hand throwing the ball to the distance of 50 m from the ground is 2.57+1.22 = 3.777 seconds
D)
[tex]v=u+at\\\Rightarrow v=0+9.81\times 2.57\\\Rightarrow v=25.2\ m/s[/tex]
The stone is moving at 25.2 m/s when it is 50m from the bottom of the building
