Answer:
v = 7.67 m/s
Explanation:
Given data:
horizontal distance 11.98 m
Acceleration due to gravity 9.8 m/s^2
Assuming initial velocity is zero
we know that
solving for t
we have
substituing all value for time t
t = 1.56 s
we know that speed is given as
v = 7.67 m/s
We make a graphic of this problem to define the angle.
The angle we can calculate through triangle relation, that is,
With this function we should only calculate the derivate in function of c
That is the rate of change of .
b) At this point we need only make a substitution of 0 for c in the equation previously found.
Hence we have finally the rate of change when c=0.
1. 12.75 J
Assuming that the force applied is parallel to the ramp, so it is parallel to the displacement of the cart, the work done by the force is
where
F = 15 N is the magnitude of the force
d = 85 cm = 0.85 m is the displacement of the cart
Substituting in the formula, we get
2. 10.6 N
In this part, the cart reaches the same vertical height as in part A. This means that the same work has been done (because the work done is equal to the gain in gravitational potential energy of the object: but if the vertical height reached is the same, then the gain in gravitational potential energy is the same, so the work done must be the same).
Therefore, the work done is
However, in this case the displacement is
d = 120 cm = 1.20 m
Therefore, the magnitude of the force in this case is