Answer:
It takes 34.173 s
Explanation:
This is a relative movement exercise.
We are going to use that :
[tex]Speed = \frac{distance}{time}[/tex]
And the relative movement velocity equation :
Given a particle P, and two reference systems A and B in which we know the velocity from system B relative to A and the velocity of P relative to B :
[tex]V_{P/A} =V_{P/B} +V_{B/A}[/tex]
Don't forget that this is a vectorial equation.In our exercise the person velocity and the speed ramp velocity have the same direction so we turn the vectorial equation into a scalar equation.
We can cover 118 m in 76 s ⇒[tex]Speed=\frac{distance}{time} \\Speed=\frac{118m}{76s} \\Speed=1.553\frac{m}{s}[/tex]
This will be our speed relative to the speed ramp
[tex]S_{person/ramp} =1.553\frac{m}{s}[/tex]
[tex]Speed_{ramp/ground} =1.9\frac{m}{s}[/tex]
We use the equation (in terms of speed) :
[tex]Speed_{person/ground} =Speed_{person/ramp} +Speed_{ramp/ground}=\\ Speed_{person/ground}=1.553\frac{m}{s} +1.9\frac{m}{s} \\ Speed_{person/ground}=3.453\frac{m}{s}[/tex]
Then →
[tex]Speed_{person/ground} =\frac{distance}{time} \\3.453\frac{m}{s} =\frac{118m}{time} \\time=\frac{118m}{3.453\frac{m}{s} } \\time=34.173s[/tex]
