Answer:
v₀ = 13.6 m/s
Explanation:
The mountain biker 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
α₀=35,2° angle v₀ above the horizontal
x = 30.1 m
y= 0
xi = 0
y₀ = 14,7 m
g= 9.8 m/s²
x-y components of v₀
v₀x= v₀*cos(35,2)°
v₀y= v₀*sin(35.2)°
Problem development
We replace data in the equation (1)
x = xi + v₀x*t
30.1 = 0 + v₀*cos(35,2)°(t )
t = (30.1) / (v₀*cos(35,2)°)
t = (36.84) /(v₀)
We replace data in the equation (2) ,
v₀y= v₀*sin(35.2)°, t = (36.84) /(v₀)
y= y₀+(v₀y)*t - (1/2)*(g)*t²
0 = 14,7 + ( v₀*sin(35.2)°)* (36.84)/(v₀)) - (1/2)*(9.8)*(36.84)²/(v₀)²
We eliminate v₀ in the term second of the rihgt
(1/2)*(9.8)*(36.84)²/(v₀)² = 14.7 + sin(35.2)° (36.84)
6650.209 = 35.9357 (v₀)²
(v₀)² = (6650.209) / (35.9357)
(v₀)² = 185.0585
[tex]v_{o} =\sqrt{185.0585}[/tex]
v₀ = 13.6 m/s
