Answer:
t = 4.218 s : stone flight time
Step-by-step explanation:
The stone describes a parabolic path.
The parabolic movement results from the composition of a uniform rectilinear motion (horizontal ) and a uniformly accelerated rectilinear motion of upward or downward motion (vertical ).
The equation of uniform rectilinear motion (horizontal ) for the x axis is :
x = xi + vx*t Equation (1)
Where:
x: horizontal position in meters (m)
xi: initial horizontal position in meters (m)
t : time (s)
vx: horizontal velocity in m/s
The equations of uniformly accelerated rectilinear motion of upward (vertical ) for the y axis are:
y= y₀+(v₀y)*t - (1/2)*g*t² Equation (2)
vfy= v₀y -gt Equation (3)
Where:
y: vertical position in meters (m)
y₀ : initial vertical position in meters (m)
t : time in seconds (s)
v₀y: initial vertical velocity in m/s
vfy: final vertical velocity in m/s
g: acceleration due to gravity in m/s²
Data
v₀ = 20.0 ° m/s , at an angle α₀=30.0° above the horizontal
y₀ = 45.0 m
g= 9.8 m/s²
Calculation of the time it takes for the stone to hit the ground
v₀y = v₀*sinα = (20 m/s)*sin(30°) = 10 m/s
We replace data in the equation (2)
y= y₀ + (v₀y)*t - (1/2)*gt²
0= 45 + (10)*(t ) - (1/2)*(9.8)(t )²
(4.9)(t )² - (10)(t ) -45 = 0
We solve the quadratic equation:
t₁ = 4.218 s
t₁ = -2.177 s
Time cannot be negative therefore t₁ = 4.218 s is the time that the stone remains in the airt.
t = 4.218 s : stone flight time