Respuesta :
Answer:
S = 8.132 m
Explanation:
∅ = 30°
Vi = 5 m/s
a = g = 3.8 m/s
we need to find horizontal and vertical component of velocity.
Vx= Vi cos∅
Vx= 5 * cos 30
Vx= 4.33 m/s
Vy= Vi sin∅
Vy= 5* sin 30
Vy= 2.5 m/s
As horizontal component of velocity will remain constant. The distance covered by potato will be:
S = Vx * t
we need to find t ( time of flight):
Time required for potato to reach maximum height:
( we will use only vertical component of velocity to find time of flight)
Vfy= Viy - g*t ( Viy= initial vertical velocity )
g * t = Viy ( Vfy= 0 at maximum height)
t₁ = Viy / g = 2.5 / 3.8 sec
t₁= 0.658 s
Height reached:
- 2gh₁ = Vfy² - Viy² ( Viy= initial vertical velocity )
( Vfy= final vertical velocity )
- 2 * 3.8 * h = ( 0 )² - (2.5 m/s)² ( ∴ Viy = 2.5 m/s & Vfy = 0 m/s)
7.6 * h₁ = 6.25
⇒ h₁ = 6.25 / 7.6
⇒ h₁ = 0.822 m
Time required to reach the ground = t₂ = ?
First find total height = H = 2 m + 0.822 m ( The potato is thrown from 2 m height )
H= 2.822 m
Now
H = Viy * t₂ + [tex]\frac{1}{2}[/tex] gt₂²
2.822= 0 * t₂ + [tex]\frac{1}{2}[/tex] *( 3.8* t₂²
2.822= 1.9 * t₂²
⇒ t₂² = 2.822/1.9 sec² = 1.485 sec²
⇒ t₂ =[tex]\sqrt{1.485 }[/tex]
⇒ t₂ = 1.22 s
Total time of flight = t = t₁ + t₂
t = 0.658 s + 1.22 s
t = 1.878 s
Now
S = Vx * t
S= 4.33 * 1.878
S = 8.132 m
