a) 7 buses
b) 6.8 m
Explanation:
a)
The motion of the motorcycle is a projectile motion, so it consists of 2 independent motions:
- A uniform motion along the horizontal direction
- A uniformly accelerated motion along the vertical direction
The initial components of the velocity of the motorcycle are:
The equation for the vertical motion of the motorcycle is
where
y is the altitude at time t
h is the initial height
is the acceleration due to gravity
The bus top is at the same height of the initial ramp, so we have
And therefore, we can solve the equation for t, to find the time of flight:
Now we find what is the horizontal distance covered by the motorcycle in its jump, which is given by:
And since each bus has a length of L = 20.0 m, the number of buses that the motorcycle can clear with its jump is:
So, 7 buses.
b)
In the previous problem, we saw that the total range of the motion of the motorcycle is
And we said that this corresponds to 7 buses.
Each bus has a length of
L = 20 m
So, the total length of 7 buses is
Therefore, the range of the motorcycle is greater than the length of the buses by:
which means he will miss the last bus by 6.8 meters.